Odd damage bonus

[Tarven]

So, I'm wielding a +1 dagger on a character with 8 strength. When the weapon was equipped in off hand, I was doing 1d3+1 damage, but when equipped on main hand, I am doing 1d3+0. The latter code should be the correct one. Not sure why I was getting the damage bonus with off hand, except that str 'bonuses' are halved in off hand, perhaps.