We are well beyond moving to 64bit on a needs-only basis. At this point it's about dropping legacy and future proofing. There's also no reason 64bit apps should have a larger memory footprint; the ISA and addressing modes are actually much tidier.

Here are the reasons they now provide a 64bit version: http://www.chiark.greenend.org.uk/~sgtatham/putty/wishlist/w...

The most likely reason is ASLR support, since you have more address space available for randomisation. Other than that, you can probably get a slight boost in performance from the differences between x64 and x86, but lose out if the code is particularly pointer-heavy.