I’ve always liked the idea of ‘leveling up’ your weapons - have some fond nerd memories of magical weapons in Earthdawn, and achieving new functionality and power by further binding the item to your character. This is somewhat similar to the elite items in recent heroes of might and magic games, slightly grindy in nature by requiring ‘item experience’, but one that I enjoyed myself.
One option to avoid the grind is through developing an ‘affinity’ with your weapon. This would not necessarily need to be linked to an individual villager, but the weapon could gain some special properties through achieving some ‘feat’. I.E. you slay a random number of Ogre’s, ergo your trusty wooden sword becomes Wooden Sword of Ogre Slaying with some appropriate +1 vs Ogres sort of modifier. This wouldn’t have to be designed around kill count or # of uses/swings/etc and could look at item time in existence, alignment of the moon, random happenstance, etc.
SteveAdamo swings the Lumpy Cotton Pillow of Geoffers Smiting
However, I’m inclined to agree with most of the other posters so far and worry that a leveling system, outside of craftables, may be outside the original intent for the game (city building and crafting - as I understand it). As you reach the appropriate skill level and have the resources available, you can either craft the new and improved weapons, or potentially have an option to ‘enhance’ your older versions (if of the same base material).