Opinions of SS pistols aside, to answer your question:
Generally speaking, a heavier bb is more stable in it's flight path. Heavier bb's will more consistently end up in the same place because they're less effected by outside influences such as wind. The further a bb travels the slower it moves and the more it can be influenced. So the benefits of a heavier bb will be most obvious at long ranges. Heavier bb's will also have an easier time punching through leaves and brush.
The brand of bb can matter more than the weight, make sure you are using a good brand of bb such as Madbull or BB Bastard. IMO .2's are more than fine for indoor plinking. For outdoor games you'll probably be fine with .25's. Try different weights for yourself and see what you prefer because it's really down to personal preference and what works best for you.
For outdoor play I use .28's in my long gun and .25's in my pistol. My pistol is a secondary and for close ranges so a lighter bb is more that suitable for how I use it. The other reason I use .25's in my pistol is because that's what I use for indoor and I don't like changing my pistol's hop-up all the time.