diff --git a/Cargo.lock b/Cargo.lock
index a612c239b0f..6ea9485d194 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -12428,6 +12428,7 @@ dependencies = [
  "sp-std",
  "sp-transaction-pool",
  "sp-version",
+ "sp-weights",
  "substrate-wasm-builder",
  "xcm",
  "xcm-builder",
@@ -12494,6 +12495,7 @@ dependencies = [
  "sp-std",
  "sp-transaction-pool",
  "sp-version",
+ "sp-weights",
  "substrate-wasm-builder",
  "xcm",
  "xcm-builder",
diff --git a/parachains/common/src/xcm_config.rs b/parachains/common/src/xcm_config.rs
index 753aa97c6fe..04f73c6b7e7 100644
--- a/parachains/common/src/xcm_config.rs
+++ b/parachains/common/src/xcm_config.rs
@@ -3,7 +3,7 @@ use core::{marker::PhantomData, ops::ControlFlow};
 use frame_support::{
 	log,
 	traits::{fungibles::Inspect, tokens::BalanceConversion, ContainsPair},
-	weights::{Weight, WeightToFee, WeightToFeePolynomial},
+	weights::Weight,
 };
 use sp_runtime::traits::Get;
 use xcm::{latest::prelude::*, CreateMatcher, MatchXcm};
@@ -95,7 +95,7 @@ impl<CurrencyBalance, Runtime, WeightToFee, BalanceConverter, AssetInstance>
 	> for AssetFeeAsExistentialDepositMultiplier<Runtime, WeightToFee, BalanceConverter, AssetInstance>
 where
 	Runtime: pallet_assets::Config<AssetInstance>,
-	WeightToFee: WeightToFeePolynomial<Balance = CurrencyBalance>,
+	WeightToFee: frame_support::weights::WeightToFee<Balance = CurrencyBalance>,
 	BalanceConverter: BalanceConversion<
 		CurrencyBalance,
 		<Runtime as pallet_assets::Config<AssetInstance>>::AssetId,
diff --git a/parachains/runtimes/assets/statemine/Cargo.toml b/parachains/runtimes/assets/statemine/Cargo.toml
index 0f0921976a8..d114d06ba02 100644
--- a/parachains/runtimes/assets/statemine/Cargo.toml
+++ b/parachains/runtimes/assets/statemine/Cargo.toml
@@ -28,6 +28,7 @@ pallet-balances = { git = "https://github.com/paritytech/substrate", default-fea
 pallet-multisig = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 pallet-proxy = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 pallet-session = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
+pallet-state-trie-migration = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master", optional = true }
 pallet-timestamp = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 pallet-transaction-payment = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 pallet-transaction-payment-rpc-runtime-api = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
@@ -44,7 +45,7 @@ sp-session = { git = "https://github.com/paritytech/substrate", default-features
 sp-std = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 sp-transaction-pool = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 sp-version = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
-pallet-state-trie-migration = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master", optional = true }
+sp-weights = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 
 # Polkadot
 kusama-runtime-constants = { git = "https://github.com/paritytech/polkadot", default-features = false, branch = "master" }
diff --git a/parachains/runtimes/assets/statemine/src/constants.rs b/parachains/runtimes/assets/statemine/src/constants.rs
index 6dccf0089ca..95e8c166a96 100644
--- a/parachains/runtimes/assets/statemine/src/constants.rs
+++ b/parachains/runtimes/assets/statemine/src/constants.rs
@@ -34,8 +34,8 @@ pub mod currency {
 /// Fee-related.
 pub mod fee {
 	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+		constants::ExtrinsicBaseWeight, FeePolynomial, Weight, WeightToFeeCoefficient,
+		WeightToFeeCoefficients, WeightToFeePolynomial,
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -55,13 +55,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Kusama, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
 			// in Statemine, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/assets/statemine/src/lib.rs b/parachains/runtimes/assets/statemine/src/lib.rs
index 446ae77bc2b..d27796b8aed 100644
--- a/parachains/runtimes/assets/statemine/src/lib.rs
+++ b/parachains/runtimes/assets/statemine/src/lib.rs
@@ -1125,3 +1125,59 @@ fn ensure_key_ss58() {
 	assert_eq!(acc, RootMigController::sorted_members()[0]);
 	//panic!("{:x?}", acc);
 }
+
+#[cfg(test)]
+mod tests {
+	use super::{constants::fee, *};
+	use crate::{CENTS, MILLICENTS};
+	use sp_runtime::traits::Zero;
+	use sp_weights::WeightToFee;
+
+	/// We can fit at least 1000 transfers in a block.
+	#[test]
+	fn sane_block_weight() {
+		use pallet_balances::WeightInfo;
+		let block = RuntimeBlockWeights::get().max_block;
+		let base = RuntimeBlockWeights::get().get(DispatchClass::Normal).base_extrinsic;
+		let transfer = base + weights::pallet_balances::WeightInfo::<Runtime>::transfer();
+
+		let fit = block.checked_div_per_component(&transfer).unwrap_or_default();
+		assert!(fit >= 1000, "{} should be at least 1000", fit);
+	}
+
+	/// The fee for one transfer is at most 1 CENT.
+	#[test]
+	fn sane_transfer_fee() {
+		use pallet_balances::WeightInfo;
+		let base = RuntimeBlockWeights::get().get(DispatchClass::Normal).base_extrinsic;
+		let transfer = base + weights::pallet_balances::WeightInfo::<Runtime>::transfer();
+
+		let fee: Balance = fee::WeightToFee::weight_to_fee(&transfer);
+		assert!(fee <= CENTS, "{} MILLICENTS should be at most 1000", fee / MILLICENTS);
+	}
+
+	/// Weight is being charged for both dimensions.
+	#[test]
+	fn weight_charged_for_both_components() {
+		let fee: Balance = fee::WeightToFee::weight_to_fee(&Weight::from_parts(10_000, 0));
+		assert!(!fee.is_zero(), "Charges for ref time");
+
+		let fee: Balance = fee::WeightToFee::weight_to_fee(&Weight::from_parts(0, 10_000));
+		assert_eq!(fee, CENTS, "10kb maps to CENT");
+	}
+
+	/// Filling up a block by proof size is at most 30 times more expensive than ref time.
+	///
+	/// This is just a sanity check.
+	#[test]
+	fn full_block_fee_ratio() {
+		let block = RuntimeBlockWeights::get().max_block;
+		let time_fee: Balance = fee::WeightToFee::weight_to_fee(&block.without_proof_size());
+		let proof_fee: Balance = fee::WeightToFee::weight_to_fee(&block.without_ref_time());
+
+		let proof_o_time = proof_fee.checked_div(time_fee).unwrap_or_default();
+		assert!(proof_o_time <= 30, "{} should be at most 30", proof_o_time);
+		let time_o_proof = time_fee.checked_div(proof_fee).unwrap_or_default();
+		assert!(time_o_proof <= 30, "{} should be at most 30", time_o_proof);
+	}
+}
diff --git a/parachains/runtimes/assets/statemint/Cargo.toml b/parachains/runtimes/assets/statemint/Cargo.toml
index f6d54cbd85f..89d08d23ab3 100644
--- a/parachains/runtimes/assets/statemint/Cargo.toml
+++ b/parachains/runtimes/assets/statemint/Cargo.toml
@@ -44,6 +44,7 @@ sp-session = { git = "https://github.com/paritytech/substrate", default-features
 sp-std = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 sp-transaction-pool = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 sp-version = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
+sp-weights = { git = "https://github.com/paritytech/substrate", default-features = false, branch = "master" }
 
 # Polkadot
 pallet-xcm = { git = "https://github.com/paritytech/polkadot", default-features = false, branch = "master" }
diff --git a/parachains/runtimes/assets/statemint/src/constants.rs b/parachains/runtimes/assets/statemint/src/constants.rs
index 393f62858cd..35e7f03695b 100644
--- a/parachains/runtimes/assets/statemint/src/constants.rs
+++ b/parachains/runtimes/assets/statemint/src/constants.rs
@@ -34,12 +34,13 @@ pub mod currency {
 /// Fee-related.
 pub mod fee {
 	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+		constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+		WeightToFeeCoefficients, WeightToFeePolynomial,
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
 	pub use sp_runtime::Perbill;
+	use sp_weights::Weight;
 
 	/// The block saturation level. Fees will be updates based on this value.
 	pub const TARGET_BLOCK_FULLNESS: Perbill = Perbill::from_percent(25);
@@ -55,13 +56,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Polkadot, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
 			// in Statemint, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/assets/statemint/src/lib.rs b/parachains/runtimes/assets/statemint/src/lib.rs
index c3813d2a7f4..7bc1dbbc160 100644
--- a/parachains/runtimes/assets/statemint/src/lib.rs
+++ b/parachains/runtimes/assets/statemint/src/lib.rs
@@ -1077,3 +1077,59 @@ cumulus_pallet_parachain_system::register_validate_block! {
 	BlockExecutor = cumulus_pallet_aura_ext::BlockExecutor::<Runtime, Executive>,
 	CheckInherents = CheckInherents,
 }
+
+#[cfg(test)]
+mod tests {
+	use super::{constants::fee, *};
+	use crate::{CENTS, MILLICENTS};
+	use sp_runtime::traits::Zero;
+	use sp_weights::WeightToFee;
+
+	/// We can fit at least 1000 transfers in a block.
+	#[test]
+	fn sane_block_weight() {
+		use pallet_balances::WeightInfo;
+		let block = RuntimeBlockWeights::get().max_block;
+		let base = RuntimeBlockWeights::get().get(DispatchClass::Normal).base_extrinsic;
+		let transfer = base + weights::pallet_balances::WeightInfo::<Runtime>::transfer();
+
+		let fit = block.checked_div_per_component(&transfer).unwrap_or_default();
+		assert!(fit >= 1000, "{} should be at least 1000", fit);
+	}
+
+	/// The fee for one transfer is at most 1 CENT.
+	#[test]
+	fn sane_transfer_fee() {
+		use pallet_balances::WeightInfo;
+		let base = RuntimeBlockWeights::get().get(DispatchClass::Normal).base_extrinsic;
+		let transfer = base + weights::pallet_balances::WeightInfo::<Runtime>::transfer();
+
+		let fee: Balance = fee::WeightToFee::weight_to_fee(&transfer);
+		assert!(fee <= CENTS, "{} MILLICENTS should be at most 1000", fee / MILLICENTS);
+	}
+
+	/// Weight is being charged for both dimensions.
+	#[test]
+	fn weight_charged_for_both_components() {
+		let fee: Balance = fee::WeightToFee::weight_to_fee(&Weight::from_parts(10_000, 0));
+		assert!(!fee.is_zero(), "Charges for ref time");
+
+		let fee: Balance = fee::WeightToFee::weight_to_fee(&Weight::from_parts(0, 10_000));
+		assert_eq!(fee, CENTS, "10kb maps to CENT");
+	}
+
+	/// Filling up a block by proof size is at most 30 times more expensive than ref time.
+	///
+	/// This is just a sanity check.
+	#[test]
+	fn full_block_fee_ratio() {
+		let block = RuntimeBlockWeights::get().max_block;
+		let time_fee: Balance = fee::WeightToFee::weight_to_fee(&block.without_proof_size());
+		let proof_fee: Balance = fee::WeightToFee::weight_to_fee(&block.without_ref_time());
+
+		let proof_o_time = proof_fee.checked_div(time_fee).unwrap_or_default();
+		assert!(proof_o_time <= 30, "{} should be at most 30", proof_o_time);
+		let time_o_proof = time_fee.checked_div(proof_fee).unwrap_or_default();
+		assert!(time_o_proof <= 30, "{} should be at most 30", time_o_proof);
+	}
+}
diff --git a/parachains/runtimes/assets/westmint/src/constants.rs b/parachains/runtimes/assets/westmint/src/constants.rs
index 8a94ad2ad9f..11e6d1bf35b 100644
--- a/parachains/runtimes/assets/westmint/src/constants.rs
+++ b/parachains/runtimes/assets/westmint/src/constants.rs
@@ -33,9 +33,12 @@ pub mod currency {
 
 /// Fee-related.
 pub mod fee {
-	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+	use frame_support::{
+		pallet_prelude::Weight,
+		weights::{
+			constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+			WeightToFeeCoefficients, WeightToFeePolynomial,
+		},
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -55,13 +58,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
-			// in Polkadot, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
-			// in Statemint, we map to 1/10 of that, or 1/100 CENT
+			// in Westend, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
+			// in Westmint, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/bridge-hubs/bridge-hub-kusama/src/constants.rs b/parachains/runtimes/bridge-hubs/bridge-hub-kusama/src/constants.rs
index c4943f85232..257d0da755b 100644
--- a/parachains/runtimes/bridge-hubs/bridge-hub-kusama/src/constants.rs
+++ b/parachains/runtimes/bridge-hubs/bridge-hub-kusama/src/constants.rs
@@ -32,9 +32,12 @@ pub mod currency {
 
 /// Fee-related.
 pub mod fee {
-	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+	use frame_support::{
+		pallet_prelude::Weight,
+		weights::{
+			constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+			WeightToFeeCoefficients, WeightToFeePolynomial,
+		},
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -51,13 +54,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Kusama, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
-			// in BridgeHub, we map to 1/10 of that, or 1/100 CENT
+			// in Bridge Hub, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/bridge-hubs/bridge-hub-polkadot/src/constants.rs b/parachains/runtimes/bridge-hubs/bridge-hub-polkadot/src/constants.rs
index de22cf7883a..388d23e6441 100644
--- a/parachains/runtimes/bridge-hubs/bridge-hub-polkadot/src/constants.rs
+++ b/parachains/runtimes/bridge-hubs/bridge-hub-polkadot/src/constants.rs
@@ -32,9 +32,12 @@ pub mod currency {
 
 /// Fee-related.
 pub mod fee {
-	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+	use frame_support::{
+		pallet_prelude::Weight,
+		weights::{
+			constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+			WeightToFeeCoefficients, WeightToFeePolynomial,
+		},
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -51,13 +54,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Polkadot, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
-			// in BridgeHub, we map to 1/10 of that, or 1/100 CENT
+			// in Bridge Hub, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/constants.rs b/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/constants.rs
index 549e549d38a..86cf8d6f7d3 100644
--- a/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/constants.rs
+++ b/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/constants.rs
@@ -30,9 +30,12 @@ pub mod currency {
 }
 
 pub mod fee {
-	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+	use frame_support::{
+		pallet_prelude::Weight,
+		weights::{
+			constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+			WeightToFeeCoefficients, WeightToFeePolynomial,
+		},
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -52,13 +55,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Rococo, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
-			// in BridgeHub, we map to 1/10 of that, or 1/100 CENT
+			// in Bridge Hub, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/lib.rs b/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/lib.rs
index bf86b16dcef..6957edc8998 100644
--- a/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/lib.rs
+++ b/parachains/runtimes/bridge-hubs/bridge-hub-rococo/src/lib.rs
@@ -46,10 +46,11 @@ use constants::currency::*;
 use frame_support::{
 	construct_runtime,
 	dispatch::DispatchClass,
+	pallet_prelude::Weight,
 	parameter_types,
 	traits::{ConstU32, ConstU64, ConstU8, Everything},
 	weights::{
-		ConstantMultiplier, Weight, WeightToFeeCoefficient, WeightToFeeCoefficients,
+		ConstantMultiplier, FeePolynomial, WeightToFeeCoefficient, WeightToFeeCoefficients,
 		WeightToFeePolynomial,
 	},
 	PalletId,
@@ -129,13 +130,44 @@ pub type Executive = frame_executive::Executive<
 ///   - Setting it to `0` will essentially disable the weight fee.
 ///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 pub struct WeightToFee;
-impl WeightToFeePolynomial for WeightToFee {
+impl frame_support::weights::WeightToFee for WeightToFee {
+	type Balance = Balance;
+
+	fn weight_to_fee(weight: &Weight) -> Self::Balance {
+		let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+		let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+		// Take the maximum instead of the sum to charge by the more scarce resource.
+		time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+	}
+}
+
+/// Maps the reference time component of `Weight` to a fee.
+pub struct RefTimeToFee;
+impl WeightToFeePolynomial for RefTimeToFee {
 	type Balance = Balance;
 	fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
-		// in Rococo, extrinsic base weight (smallest non-zero weight) is mapped to 1 MILLIUNIT:
-		// in our template, we map to 1/10 of that, or 1/10 MILLIUNIT
 		let p = MILLIUNIT / 10;
 		let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+		smallvec![WeightToFeeCoefficient {
+			degree: 1,
+			negative: false,
+			coeff_frac: Perbill::from_rational(p % q, q),
+			coeff_integer: p / q,
+		}]
+	}
+}
+
+/// Maps the proof size component of `Weight` to a fee.
+pub struct ProofSizeToFee;
+impl WeightToFeePolynomial for ProofSizeToFee {
+	type Balance = Balance;
+	fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+		// Map 10kb proof to 1/10 MILLIUNIT.
+		let p = MILLIUNIT / 10;
+		let q = 10_000;
+
 		smallvec![WeightToFeeCoefficient {
 			degree: 1,
 			negative: false,
diff --git a/parachains/runtimes/collectives/collectives-polkadot/src/constants.rs b/parachains/runtimes/collectives/collectives-polkadot/src/constants.rs
index cc41d5c6378..e9709519827 100644
--- a/parachains/runtimes/collectives/collectives-polkadot/src/constants.rs
+++ b/parachains/runtimes/collectives/collectives-polkadot/src/constants.rs
@@ -43,9 +43,12 @@ pub mod currency {
 
 /// Fee-related.
 pub mod fee {
-	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+	use frame_support::{
+		pallet_prelude::Weight,
+		weights::{
+			constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+			WeightToFeeCoefficients, WeightToFeePolynomial,
+		},
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -65,13 +68,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Polkadot, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
 			// in a parachain, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/contracts/contracts-rococo/src/constants.rs b/parachains/runtimes/contracts/contracts-rococo/src/constants.rs
index 6dccf0089ca..4598ddaa264 100644
--- a/parachains/runtimes/contracts/contracts-rococo/src/constants.rs
+++ b/parachains/runtimes/contracts/contracts-rococo/src/constants.rs
@@ -33,9 +33,12 @@ pub mod currency {
 
 /// Fee-related.
 pub mod fee {
-	use frame_support::weights::{
-		constants::ExtrinsicBaseWeight, WeightToFeeCoefficient, WeightToFeeCoefficients,
-		WeightToFeePolynomial,
+	use frame_support::{
+		pallet_prelude::Weight,
+		weights::{
+			constants::ExtrinsicBaseWeight, FeePolynomial, WeightToFeeCoefficient,
+			WeightToFeeCoefficients, WeightToFeePolynomial,
+		},
 	};
 	use polkadot_core_primitives::Balance;
 	use smallvec::smallvec;
@@ -55,13 +58,46 @@ pub mod fee {
 	///   - Setting it to `0` will essentially disable the weight fee.
 	///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 	pub struct WeightToFee;
-	impl WeightToFeePolynomial for WeightToFee {
+	impl frame_support::weights::WeightToFee for WeightToFee {
+		type Balance = Balance;
+
+		fn weight_to_fee(weight: &Weight) -> Self::Balance {
+			let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+			let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+			// Take the maximum instead of the sum to charge by the more scarce resource.
+			time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+		}
+	}
+
+	/// Maps the reference time component of `Weight` to a fee.
+	pub struct RefTimeToFee;
+	impl WeightToFeePolynomial for RefTimeToFee {
 		type Balance = Balance;
 		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
 			// in Kusama, extrinsic base weight (smallest non-zero weight) is mapped to 1/10 CENT:
 			// in Statemine, we map to 1/10 of that, or 1/100 CENT
 			let p = super::currency::CENTS;
 			let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
+			smallvec![WeightToFeeCoefficient {
+				degree: 1,
+				negative: false,
+				coeff_frac: Perbill::from_rational(p % q, q),
+				coeff_integer: p / q,
+			}]
+		}
+	}
+
+	/// Maps the proof size component of `Weight` to a fee.
+	pub struct ProofSizeToFee;
+	impl WeightToFeePolynomial for ProofSizeToFee {
+		type Balance = Balance;
+		fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+			// Map 10kb proof to 1 CENT.
+			let p = super::currency::CENTS;
+			let q = 10_000;
+
 			smallvec![WeightToFeeCoefficient {
 				degree: 1,
 				negative: false,
diff --git a/parachains/runtimes/testing/penpal/src/lib.rs b/parachains/runtimes/testing/penpal/src/lib.rs
index a727bb27dba..b3cf2e5a654 100644
--- a/parachains/runtimes/testing/penpal/src/lib.rs
+++ b/parachains/runtimes/testing/penpal/src/lib.rs
@@ -34,11 +34,12 @@ use cumulus_pallet_parachain_system::RelayNumberStrictlyIncreases;
 use frame_support::{
 	construct_runtime,
 	dispatch::DispatchClass,
+	pallet_prelude::Weight,
 	parameter_types,
 	traits::{AsEnsureOriginWithArg, ConstU32, ConstU64, ConstU8, Everything},
 	weights::{
-		constants::WEIGHT_REF_TIME_PER_SECOND, ConstantMultiplier, Weight, WeightToFeeCoefficient,
-		WeightToFeeCoefficients, WeightToFeePolynomial,
+		constants::WEIGHT_REF_TIME_PER_SECOND, ConstantMultiplier, FeePolynomial,
+		WeightToFeeCoefficient, WeightToFeeCoefficients, WeightToFeePolynomial,
 	},
 	PalletId,
 };
@@ -149,13 +150,26 @@ pub type Executive = frame_executive::Executive<
 ///   - Setting it to `0` will essentially disable the weight fee.
 ///   - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
 pub struct WeightToFee;
-impl WeightToFeePolynomial for WeightToFee {
+impl frame_support::weights::WeightToFee for WeightToFee {
+	type Balance = Balance;
+
+	fn weight_to_fee(weight: &Weight) -> Self::Balance {
+		let time_poly: FeePolynomial<Balance> = RefTimeToFee::polynomial().into();
+		let proof_poly: FeePolynomial<Balance> = ProofSizeToFee::polynomial().into();
+
+		// Take the maximum instead of the sum to charge by the more scarce resource.
+		time_poly.eval(weight.ref_time()).max(proof_poly.eval(weight.proof_size()))
+	}
+}
+
+/// Maps the reference time component of `Weight` to a fee.
+pub struct RefTimeToFee;
+impl WeightToFeePolynomial for RefTimeToFee {
 	type Balance = Balance;
 	fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
-		// in Rococo, extrinsic base weight (smallest non-zero weight) is mapped to 1 MILLIUNIT:
-		// in our template, we map to 1/10 of that, or 1/10 MILLIUNIT
 		let p = MILLIUNIT / 10;
 		let q = 100 * Balance::from(ExtrinsicBaseWeight::get().ref_time());
+
 		smallvec![WeightToFeeCoefficient {
 			degree: 1,
 			negative: false,
@@ -165,6 +179,23 @@ impl WeightToFeePolynomial for WeightToFee {
 	}
 }
 
+/// Maps the proof size component of `Weight` to a fee.
+pub struct ProofSizeToFee;
+impl WeightToFeePolynomial for ProofSizeToFee {
+	type Balance = Balance;
+	fn polynomial() -> WeightToFeeCoefficients<Self::Balance> {
+		// Map 10kb proof to 1 CENT.
+		let p = MILLIUNIT / 10;
+		let q = 10_000;
+
+		smallvec![WeightToFeeCoefficient {
+			degree: 1,
+			negative: false,
+			coeff_frac: Perbill::from_rational(p % q, q),
+			coeff_integer: p / q,
+		}]
+	}
+}
 /// Opaque types. These are used by the CLI to instantiate machinery that don't need to know
 /// the specifics of the runtime. They can then be made to be agnostic over specific formats
 /// of data like extrinsics, allowing for them to continue syncing the network through upgrades