|Soul Gadget Radiant - Main character is connected with his weapon. People around him can't figure out why he has such a weapon, when even he doesn't understand....
This would be a little bit of a stretch, but I would also recommend MÄR, not because of the character but the weapon. The weapon, itself, has no memory of its past, but it actually
Spoiler (mouse over to view)
....once belonged to someone powerful.
Looking for memory related manga/manhwa? -> click me