well my title and description kinda say it all

There are two factors: The damage stat on the weapon and the strength of the wielder. Damage stat increases the damage dealt in a linear (unconfirmed) fashion, while increasing strength points has diminishing returns past a certain point (13 or 14). Skill ranks in Combat are rumored to help as well, but I haven't confirmed this either.

I am fairly certain I also noticed an increase in damage once I transed my spec skill.

Knighthood+Specialisation, and also to lesser extent Combat, increase weapon damage, speed and wounding. I thought it's common knowledge. (that comment directed at Tervic, not AlexRey)

If you plan to have hunting weapons, look at speed rather than damage. The damage stat doesn't increase the damage dealt that much in PvE - there is an increase, but you'll have better damage-per-second with high speed weapons.

Want about monk weapons, have we even begun to be able to figure those out?

It's not common to -my- brain at least I knew knighthood & spec increased damage and wounding, but I didn't know they affected speed too. Then again, a lot of the secondary benefits from investing in skills isn't written down anywhere.