diff --git a/swh/web/browse/snapshot_context.py b/swh/web/browse/snapshot_context.py
--- a/swh/web/browse/snapshot_context.py
+++ b/swh/web/browse/snapshot_context.py
@@ -485,7 +485,11 @@
 
     releases = list(reversed(releases))
 
-    snapshot_sizes = archive.lookup_snapshot_sizes(snapshot_id)
+    snapshot_sizes_cache_id = f"swh_snapshot_{snapshot_id}_sizes"
+    snapshot_sizes = cache.get(snapshot_sizes_cache_id)
+    if snapshot_sizes is None:
+        snapshot_sizes = archive.lookup_snapshot_sizes(snapshot_id)
+        cache.set(snapshot_sizes_cache_id, snapshot_sizes)
 
     is_empty = sum(snapshot_sizes.values()) == 0
 
diff --git a/swh/web/common/archive.py b/swh/web/common/archive.py
--- a/swh/web/common/archive.py
+++ b/swh/web/common/archive.py
@@ -985,7 +985,7 @@
     return converters.from_origin_visit({**visit_status.to_dict(), "type": visit.type})
 
 
-def lookup_snapshot_sizes(snapshot_id):
+def lookup_snapshot_sizes(snapshot_id: str) -> Dict[str, int]:
     """Count the number of branches in the snapshot with the given id
 
     Args:
@@ -1003,23 +1003,49 @@
         snapshot_sizes["release"] = 0
     # adjust revision / release count for display if aliases are defined
     if "alias" in snapshot_sizes:
-        aliases = lookup_snapshot(
-            snapshot_id, branches_count=snapshot_sizes["alias"], target_types=["alias"]
-        )
-        for alias in aliases["branches"].values():
-            try:
-                for target_type in ("revision", "release"):
-                    snapshot = lookup_snapshot(
+        # iterate on all snapshot branches to resolve aliases but stop once
+        # all aliases have been processed
+        batch_size = 10000
+        snapshot = lookup_snapshot(snapshot_id, branches_count=batch_size)
+        nb_processed_aliases = 0
+        while snapshot is not None:
+            for branch_name, branch_info in snapshot["branches"].items():
+                if branch_info["target_type"] == "alias":
+                    nb_processed_aliases += 1
+                    branches = lookup_snapshot(
                         snapshot_id,
-                        branches_from=alias["target"],
+                        branches_from=branch_info["target"],
                         branches_count=1,
-                        target_types=[target_type],
-                    )
-                    if snapshot and alias["target"] in snapshot["branches"]:
-                        snapshot_sizes[target_type] += 1
-            except NotFoundExc:
-                # aliased revision or release is missing in the snapshot
-                pass
+                    )["branches"]
+                    if (
+                        branch_info["target"] in branches
+                        and branches[branch_info["target"]] is not None
+                    ):
+                        target = branches[branch_info["target"]]["target"]
+                        for lookup_fn, target_type in (
+                            (lookup_revision, "revision"),
+                            (lookup_release, "release"),
+                        ):
+                            try:
+                                lookup_fn(target)
+                                snapshot_sizes[target_type] += 1
+                                break
+                            except NotFoundExc:
+                                # aliased revision or release is missing in the snapshot
+                                pass
+                    if nb_processed_aliases == snapshot_sizes["alias"]:
+                        break
+            if nb_processed_aliases == snapshot_sizes["alias"]:
+                break
+            if snapshot["next_branch"] is not None:
+                snapshot = lookup_snapshot(
+                    snapshot_id,
+                    branches_from=snapshot["next_branch"],
+                    branches_count=batch_size,
+                )
+            else:
+                snapshot = None
+
         del snapshot_sizes["alias"]
         # remove possible None key returned by snapshot_count_branches
         # when null branches are present in the snapshot