I just did a little test.

I took off all my weapons, and tried to use my Blast Charge ability.Didn't work, I must have a weapon.

So I put a weapon on my main slot, and checked the damage.

Then I changed the weapon in my main slot, and checked the damage. It was more or less the same. The two weapons differed by about 2 points damage.

Then I removed all melee weapons, and used the Bow which was even more damage...and the result was the same.

To me, regardless of what weapon I used in my slots, the resulting damage was constant. So..how does 'Weapon Damage' work?

If I have a main hand and an off-hand weapon, which does it use?
What if I have a Bow or Gun equipped that does more damage...which does it use?