Put your weapon on the forge. If your aim is good enough, you may be able to repair or improve it.
Example: create a knife.put the knife on the forge
How much improvement depends on your aim skill. Each tick, a random number is generated between 0 and your aim plus 10. If the number is greater than your weapon's health, then the weapon will be repaired a bit. After the weapon's health is fully repaired, the process will (hopefully) start improving the healthmax, allowing it to deal more damage per hit.
Once you feel the weapon is about as good as you can make it, get it or wield it and the improvement process will end.