A bit late, but here's a relevant use case:
I need to cache two types of objects: large (deserialised) data files that take 10 minutes to load and cost 15G of ram each, and smaller (dynamically compiled) objects that contain internal references to those data files (the smaller objects are also cached because they take ~10s to generate). These caches are hidden within the factories that supply the objects (the former component having no knowledge of the latter), and have different eviction policies.
When my `data file' cache evicts an object, it replaces it by a weak reference, so if that object is still available when next requested, we can resurrect it (and renew its cache timeout). In this way we avoid losing (or accidentally duplicating) any object before it is truly defunct (i.e. not used anywhere else). Notice that neither cache is required to be aware of the other, and that no other client objects need to be aware that there are any caches at all (eg: we avoid needing 'keepalives', callbacks, registration, retrieve-and-return scopes, etc - things get a lot simpler).
So although using WeakReference by itself (instead of a cache) is a terrible idea (because modern GCs are typically tuned to the size of the L2 CPU cache, and regular code will burn through this many times per minute), it's very useful as a way to hide your caches from the rest of your code.