There are many ways to upgrade your weapon! The simplest way is to use them so they gain XP and level up during raids!     
Leveling your weapon increases Handling, Mobility and the kicker... Damage!     
You can always check your Items Progress under the Upgrade Tree found in Upgrade / Modify.

Gem Fragments

Gem Fragments can be found while playing raids, every enemy has a chance to drop them.     
Optional Objectives are tasked at the start of raids and completing these will reward you with Gem Fragments!     
Fragments come from doing raids and grinding Gems, these fragments can be used to upgrade armored chest pieces and purchase items during raid from the Wandering Merchant.     
You can fuse Gem Fragments together to create gems, and they are used to upgrade a gem to a higher rarity. You can also reverse this process, at a high loss.


There are many different unique weapon/equipment variants, these may give bonuses to the item, so pay attention to those!     
Antique boosts the weapon stats by 1.     
Spooky, Eggy, Molten and Snowy prefixes also boost the weapon stats by 1 too. These can be gained during their respective time of year events! or with an Eventifier!     
                                      As well as Homemade, which also boots the weapons stats by +1 to stats or potions and food by 10% by crafting with only farmed/mined parts! (Will say Homemade on the parts!)

             Not only that but you can use 999x gold bar to make a Goldifier which applies +1 stats to your weapon also turns your weapon/ item solid gold upon use of the necessary gold.

     This is reachable by visiting the Fabrication bench next to holo-Kleiner.

Boss Essence

Boss Essence can be found during world bosses. The essence dropped will match the boss encountered during the world boss event.     
Boss Essence can be applied to equipment to add the corresponding boss set modifier.     
You can Condense boss set items into boss tears which can then be fused into Boss Essence.

Related Topics: 2.1 Rarities, 2.2 Stat Mutators, 2.3 Attributes & Gems, 2.4 Blessings, Sigils & Sockets, 2.5 Tech, Tiers & Mods, 2.6 Vorpal, Xen & Void Shards, 2.7 Pets, 2.8 Soulbound