Do Hits wear out weapon tags or weapons? I mean to say that I wonder when a sword becomes less effective for example.

The game doesn't concern itself with that (or even what gear does outside of tags). You could (if you wanted) have tags on gear be ones you can cross off when you suffer a setback, after which the gear would be destroyed (if it was out of tags). If I ever do an appendix, maybe I'll include this idea.