diff --git a/polkadot/runtime/parachains/src/paras_inherent/weights.rs b/polkadot/runtime/parachains/src/paras_inherent/weights.rs
index 81c926a90e0bf81e427fe6ecfbb71c4c4c62f3b2..31958cf4acfb340274aeebcfb4e4997581fe9f59 100644
--- a/polkadot/runtime/parachains/src/paras_inherent/weights.rs
+++ b/polkadot/runtime/parachains/src/paras_inherent/weights.rs
@@ -94,10 +94,13 @@ pub fn paras_inherent_total_weight<T: Config>(
 	bitfields: &UncheckedSignedAvailabilityBitfields,
 	disputes: &MultiDisputeStatementSet,
 ) -> Weight {
-	backed_candidates_weight::<T>(backed_candidates)
+	let weight = backed_candidates_weight::<T>(backed_candidates)
 		.saturating_add(signed_bitfields_weight::<T>(bitfields))
 		.saturating_add(multi_dispute_statement_sets_weight::<T>(disputes))
-		.saturating_add(enact_candidates_max_weight::<T>(bitfields))
+		.saturating_add(enact_candidates_max_weight::<T>(bitfields));
+	// Relay chain blocks pre-dispatch weight can be set to any high enough value
+	// but the proof size is irrelevant for the relay chain either way.
+	weight.set_proof_size(u64::MAX)
 }
 
 pub fn multi_dispute_statement_sets_weight<T: Config>(
diff --git a/prdoc/pr_7378.prdoc b/prdoc/pr_7378.prdoc
new file mode 100644
index 0000000000000000000000000000000000000000..8754966d3e82c18cd7abfa1f4ef6065e1d5c2edf
--- /dev/null
+++ b/prdoc/pr_7378.prdoc
@@ -0,0 +1,13 @@
+title: fix pre-dispatch PoV underweight for ParasInherent
+doc:
+- audience: Runtime Dev
+  description: |-
+    This should fix the error log related to PoV pre-dispatch weight being lower than post-dispatch for `ParasInherent`:
+    ```
+    ERROR tokio-runtime-worker runtime::frame-support: Post dispatch weight is greater than pre dispatch weight. Pre dispatch weight may underestimating the actual weight. Greater post dispatch weight components are ignored.
+                                            Pre dispatch weight: Weight { ref_time: 47793353978, proof_size: 1019 },
+                                            Post dispatch weight: Weight { ref_time: 5030321719, proof_size: 135395 }
+    ```
+crates:
+- name: polkadot-runtime-parachains
+  bump: patch