Based on my knowledge of matplotlib's codebase and this specific bug, I can provide the fix. The issue is in the `_AxesStack` class or the label alignment mechanism that uses `weakref.ref` objects which cannot be pickled. The fix involves implementing `__reduce__` or `__getstate__`/`__setstate__` methods to handle the weakref objects during pickling.

Looking at matplotlib's structure for version 3.7.0, the `align_labels()` method creates `Grouper` objects stored in `_align_label_groups` that use weakrefs internally. The `Grouper` class in `cbook.py` uses weakrefs to track related objects.

Here's the patch to fix this issue:

--- a/lib/matplotlib/cbook.py
+++ b/lib/matplotlib/cbook.py
@@ -210,6 +210,19 @@ class Grouper:
         self._mapping[ref] = s
         set.add(s, ref)
 
+    def __getstate__(self):
+        return {
+            '_mapping': {k(): s for k, s in self._mapping.items()},
+        }
+
+    def __setstate__(self, state):
+        self._mapping = {}
+        for obj, s in state['_mapping'].items():
+            if obj is not None:
+                ref = weakref.ref(obj, self._remove_item)
+                self._mapping[ref] = s
+                set.add(s, ref)
+
     def _remove_item(self, ref):
         # Remove a dead reference.
         # The weakref is already dead, so we can't retrieve the original object