The damage shown on the website (and in your inventory in game) is the base damage that the weapon deals. It is a static number that goes into the damage equation when you attack. Your stats are variables that change the equation. Power strike/throw/draw multiply the damage of the weapon (each one does so by a different %).
For a heavy throwing axe and 4 PT, you would do 47c [base damage] plus 40% [4 x 10%] because PT increases damage by 10% per level. That totals to 47 x 1.4 = 65.8c damage.
Weapons proficiency (and strength for melee weapons, don't think thrown includes it but I may be wrong) increase damage by a small percent (~5% at the highest attainable levels) as well. More important than that is the speed bonus. If your target is running away from the thrown axe they will take less damage than if they stood still. If they are charging towards you they will take more damage than if they were standing still. This is why ranged weapons can take down a charging horse in very few or even a single shot.
Hope that helps!