By completing weapon mastery gigs you can earn weapon styles. In order to unlock a weapon mastery gig you need to first reach max level on the weapon.
Tier 1 mastery gigs require you to get a specific number of kills with the weapon. Once completed you'll unlock the Alloy stye for the weapon.
After completing a weapon's Tier 1 mastery gig you'll unlock the Tier 2 mastery gig for the weapon. Tier 2 mastery gigs require getting specific types of kills such as precision kills (headshots), kills while crouching/sliding or even double kills. Once a weapon's Tier 2 mastery gig is completed you'll unlock the Ingot style for the weapon.