ok, a lvl 55 posted this so he had it equipt. The dmg bonus is what he gets when equipting it. As far as i can tell starting at lvl 28 for all melee classes you get 1dmg bonus every 3 lvl's. It is not exact to that but along those lines. My lvl 35 has dmg bonus of 3 so far.
For one hand weapons, it is (CurrentLevel - 25) / 3...rounded down to a whole number. At level 35, it is (35 - 25) / 3, which is 3.33 rounded down to 3.