I would expand this by having the damage die increase at BAB 6, 11, and 16. So a dagger is a 1d4 weapon wielded by a 1st level fighter, a 1d6 weapon by a 6th level fighter, a 1d8 weapon when wielded by an 11th level fighter, and a 2d6 weapon when wielded by 16th level fighter.
Weapon...