diff --git a/src/compute/src/extensions/arrange.rs b/src/compute/src/extensions/arrange.rs
index 56987ae2b4dfc..c9616c83a924c 100644
--- a/src/compute/src/extensions/arrange.rs
+++ b/src/compute/src/extensions/arrange.rs
@@ -8,7 +8,7 @@
 // by the Apache License, Version 2.0.
 
 use std::collections::BTreeMap;
-use std::rc::Rc;
+use std::rc::{Rc, Weak};
 
 use differential_dataflow::difference::Semigroup;
 use differential_dataflow::lattice::Lattice;
@@ -272,14 +272,19 @@ where
             ));
 
             // Weak references to batches, so we can observe batches outside the trace.
-            let mut batches = BTreeMap::new();
+            // Batches are immutable once sealed, so we compute their size exactly
+            // once (when first observed) and cache it alongside the weak reference.
+            // Subsequent activations only sum the cached values for live batches,
+            // avoiding a repeated walk of every batch's backing regions.
+            let mut batches: BTreeMap<*const B, (Weak<B>, (usize, usize, usize))> = BTreeMap::new();
 
             move |input, output| {
                 input.for_each(|time, data| {
-                    batches.extend(
-                        data.iter()
-                            .map(|batch| (Rc::as_ptr(batch), Rc::downgrade(batch))),
-                    );
+                    for batch in data.iter() {
+                        batches
+                            .entry(Rc::as_ptr(batch))
+                            .or_insert_with(|| (Rc::downgrade(batch), logic(batch)));
+                    }
                     output.session(&time).give_container(data);
                 });
                 let Some(trace) = trace.upgrade() else {
@@ -287,13 +292,15 @@ where
                 };
 
                 trace.borrow().trace().map_batches(|batch| {
-                    batches.insert(Rc::as_ptr(batch), Rc::downgrade(batch));
+                    batches
+                        .entry(Rc::as_ptr(batch))
+                        .or_insert_with(|| (Rc::downgrade(batch), logic(batch)));
                 });
 
                 let (mut size, mut capacity, mut allocations) = (0, 0, 0);
-                batches.retain(|_, weak| {
-                    if let Some(batch) = weak.upgrade() {
-                        let (sz, c, a) = logic(&batch);
+                batches.retain(|_, (weak, cached)| {
+                    if weak.strong_count() > 0 {
+                        let (sz, c, a) = *cached;
                         (size += sz, capacity += c, allocations += a);
                         true
                     } else {