Open for thoughts, but might make training slightly more interesting. Could drop something along the lines of "smooth stones" and "weight stones" that can be added on to weapons for minor short term damage increases. Thinking smooth for sharp weapons and weight for blunt.
The other option here is to make this a permanent increase. One stone allowed per weapon. This could make the progression through the weapons a little less linear as you may not want to replace earlier weapons with small upgrades.
These stones would have to sit in your stash until applied, and depending on rarity could be worth some reasonable value should you wish to sell them.
This also opens up ideas along the lines of health stealing and small stat buffs on weapons should we ever decide to go down that route.