Strength powers should affect it, because otherwise it is pretty worthless for anything with a strength power. Otherwise you've spent 2 refresh on a crappy pistol (shorter range) that you can hide really well (but that doesn't mean you always have access to it, bad guys can find a way to make sure you can't use it whether muzzling your mouth or whatever). Sure, you can theoretically run out of ammo, but that almost never happens. Overall that's garbage when a high strength character can just have a few throwing axes to lug around and they'll be weapon 2+strength bonuses (I believe a throwing axe would do more damage than a dagger). Or they can pick up things on the scene and toss them due to their high strength (heck, isn't that hard to throw PEOPLE as weapons). Heck, they'll pretty much get just as much mileage out of a bag of baseballs as they would a breath weapon (they can take those baseballs just about anywhere, and we could consider them weapon 0 as a base if we wanted) and that's just with INHUMAN strength.
For 2 refresh, it should scale with anything that increases weapon damage, otherwise it is a joke. Heck, 2 refresh is pretty expensive as it is...I'm not entirely convinced it shouldn't be just 1 refresh. (I'd say claws are similar and should be 0 refresh, except they give you an excellent weapon for the fist skill, which is pretty nice given some of the stunts available for fists).