When you first acquire a weapon, it’s at level 1. You can gradually level a gun up to level 5, which improves its damage output, ammo capacity, and several of its secondary stats such as effect radius or rate of fire.
Once a weapon’s reached level 2, you’re also able to equip it with a Weapon Amp, expanding its capabilities. Weapon Amps are dealt with in detail in the section following this one, but for now it’s enough to know that it’s a potentially lethal modification.
Earning XP with most guns requires that you inflict damage, and the more damage the guns do, the faster they level. If you want to power-level a new gun, your best bet is to deliberately hunt down whatever class of enemy it’s strongest against.