What upgrade increases damage?

This is gonna be a long answer but here we go. Upgrading your ammo and muzzle increases damage for your weapon when using gold coins. The body might too, I don't remember. It's been a while since I've had to upgrade.

When you have purchased (with gold coins) all of the standard upgrades, you can continue to upgrade using battle tokens (blue tokens earned from PvP, Range Challenge and Arena Challenge or purchased in the store). Use them to upgrade muzzle, ammo, body and grip and all of those upgrades increase your damage.

When playing PvP you can further increase the damage for your weapon by buying a pattern from the gear menu. Hope that answers your question.