Too grindy - maybe. With my level of skill, it took me about 60 hours to reach lvl 40 for the first weapons of every class (admittedly, I just play and do not grind for XP). The gap - no, I wouldn't say so. The upgrades you get for reaching lvl 5-8 for a gun are the best in my opinion, and after them, I rarely change anything.
As for the progressing, you literally earn points - all kinds of points - while holding the gun in your hands. Even if you capture the flag, the score you earn goes into the gun's experience. There are no "special" actions you need to perform to unlock some parts.
