If the weapon has an attached Sumulacra with it, it means that it can be levelled up to get more powers. Most weapons have different status effects, with the base status effect having a similar buff. However, each weapon has its advancement powerups, specializing the weapon in different ways. You can look at the weapon and their powerups for each advancement level by heading into the weapons section on the main menu, and then clicking on the weapons tab. Finally, you can head to the Warehouse and browse all the weapons in the game. Take note of what each weapon does, as they all serve different purposes, from shield busting, to pure DPS weaponry.

Also, to level these weapons up, you will need to collect duplicates of each weapon. The duplicates will then provide a core with the associated weapon name. You can then use these to upgrade the weapons through the advancement section. You can also get advancement cores from the store by buying them using Black Gold from the weapons store to speed up your levelling. If you want to level these weapons by being free-to-play, you need to make sure you get your weekly missions done, and get the Type III chip, which allows you to open up loot boxes from the World Bosses, especially for the SSR weapons.