I like to use different rules for damage in my games. Instead of using the default rules I have the Attacker and Target roll their attack rolls as usual. If the Attacker rolls equal or higher to their target, they can roll for damage. To handle this, I have 3 weapon power levels.
A Level One weapon deals 1d4 damage. A Level Two weapon deals 2d4 damage. A Level Three weapon deals 3d4 damage. A player with no weapon and no specialisms that imply physical strength or combat training/martial arts deals 1 damage per attack.
You could make things interesting by having martial arts or unarmed combat specialisms add to the base 1 damage. You can use even higher level weapons but the numbers can get pretty crazy so they don't work great with default HP. If a player has a healing skill I like to have them make a d4 roll to see how much they heal their Target for.
The USR (Unbelievably Simple Roleplaying) System belongs to Scott Malthouse and Trollish Delver Games