When you look at your character sheet, you should see an ATK (attack) stat. Increasing that stat increases the max damage you can do. Your weapon skills and offense skill increase your ATK. That is why you are seeing your max damage go up as your skills go up.
Increasing your strength also increases your ATK, which is why melee DPS classes want to stack strength. Once your strength, weapon skills, and offense skills are capped, your only way to increase ATK is with buffs or worn effects that increase ATK directly. This is why melees love the Aura of Battle worn effect, for example. Each item you wear with Aura of Battle gives you +10 ATK, even if your strength and skills are capped. The blazing gauntlets from Ragefire have worn firefist, which is another +7 or so. And a few buffs increase ATK, like grim aura, which is easy to obtain with a shrunken goblin earring.
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