This is going to be really short.
If you roll a “1” for damage, reduce the weapon’s damage die by one step.
This rewards bigger weapons with better durability, and is simple and quick. In essence, the “1” damage does not represent a weak hit, but rather a strong one hitting in a bad spot. You could also link it to the armor of the target struck (for complexity), but then you’d probably have to add in something like a breakage roll too. Armor could possibly work in a similar way.