There are hundreds of weapons in Godfall, but there is always a good chance of falling in love with one of them, and wanting to bring it with you are work through the game. Fortunately, Godfall does have a pretty robust weapon upgrade system in place.
To get access to the system, called The Forge, you will need to play through the Earth area story until you meet a character called Zenun. After rescuing him, he will return to the Sanctum and you will then have access to the Forge.
To upgrade a weapon, or any other item in your inventory, interact with the Forge and then select the item you wish to Upgrade from the inventory there. At the bottom right of the screen you will see a number of prompts. Hit the one for Upgrade, or click on Upgrade on PC, and you will be shown the resources that you need to upgrade the weapon.
As long as you have the resources, you can upgrade the weapon by one level. The maximum number of upgrades a weapon can take is indicated by a number of dots on the top left of the rightmost weapon card, shown above. This will give you extra damage from the weapon.
If you really like a weapon, you can Enchant it. This will increase the rarity level, giving more weapon bonuses, a large damage increase, and maybe even giving you a new bonus from the additional rarity level.
Doing this works just the same as upgrading, except you choose the Enchant option. It also has a much higher resource costs, and the resources you need are harder to find in the game, so you won’t be able to do it too often. As such, wait until you are sure you really like a weapon before Enchanting it. For the most part, you want to Enchant weapons that give good bonuses for specific builds.