My Weapon Is the Weakest but Apparently It Levels Up

I, a NEET, turn my life around from one of constant oppression to become the mightiest hero—and the secret lies in… a battered, broken “weakest weapon”?! It was the only weapon in this world with the ability to level up. This is the story of how a protagonist, once mocked as a failure, becomes a hero who saves the world alongside the weakest weapon!

(Source: Ganma!, translated)

Note: Includes one extra chapter.