I understand that weak references are at the mercy of the garbage collector, and we cannot guarantee that the weak reference will exist. I could not see a need to have weak reference, but sure there should be a reason.
It's actually quite often a bad idea to use weak hashmaps. For one it's easy to get wrong, but even worse it's usually used to implement some kind of cache.
What this does mean is the following: Your program runs fine with good performance for some time, under stress we allocate more and more memory (more requests = more memory pressure = probably more cache entries) which then leads to a GC.
Now suddenly while your system is under high stress you not only get the GC, but also lose your whole cache, just when you'd need it the most. Not fun this problem, so you at least have to use a reasonably sized hard referenced LRU cache to mitigate that problem - you can still use the weakrefs then but only as an additional help.
I've seen more than one project hit by that "bug"..