On the subject of her Machine Gun being at lv 1, I think that's because experience crystals represent becoming more proficient at using a weapon. Obviously its bullets don't get bigger just because you're getting better with it, that's just gameplay (which level is "canon" is based on preference).
Curly's Machine Gun is at level 1 and requires charging because of her inexperience with it. This might be just me, but I always saw her as rather less competent at combat then Quote, possibly because of her time taking care of Mimiga softening her besides the obvious inexperience she gets thanks to amnesia. Sure, she likely had to use the gun to stave off the usual Sand Zone fauna, but it's possible she didn't really use it unless necessary.
Quote, on the other hand, has been running around and shooting things almost since waking up while only armed with a simple energy pistol, so he's much more skilled than her. When she teams up with Quote in the labyrinth, her weapon is at lv 3 because she has more experience with it from all the Gaudi and resolve to get her kids back (how sad that that never happens...).
It may be that her Nemesis works as well as it does because, unlike other weapons, it's powerful but also fragile, so if you push it too hard it will temporarily deliver much less punch. Quote is naturally trigger happy and has to be gentler than usual with it, but Curly is used to being more methodical with her shots and using the Nemesis comes naturally for her.
Well, that's my take on it, anyway...