Stranger of Paradise: Final Fantasy Origin is a game where you will find yourself showered with free gear. You will constantly get new weapons and armor while running through dungeons, but just swapping out your weapon isn't everything in the game. If you want to make truly powerful weapons, then you need to enhance them.
To upgrade your weapons, you need to move over to the Cornelia tab and choose the Smithy option. You will now see two options, one for dismantling armor and weapons and one that lets you upgrade them. You want to choose the Upgrade Special Effect option which will open up a menu that shows all of your weapons.
Related: All Stats in Stranger of Paradise: Final Fantasy Origin and what they mean, explained
Once you scroll to your desired weapon, you can press the interact button to take a closer look at the stats you can enhance. Choose the stat you want to upgrade and how much you want to upgrade it, and the game will tell you the material cost. If you have the materials, press the interact button again to upgrade.
Materials are collected through dismantling gear and you can see what items you get from each piece before you dismantle them.
For more on Stranger of Paradise, check out How to disassemble gear in Stranger of Paradise: Final Fantasy Origin on Pro Game Guides!