I have very vague memories of a game where you played... I think it was a barbarian? I remember the weapon could be upgraded but I don't remember how! The graphics looked basic even for the time.
I mean, you've described just about everything from Castle of the Winds to Skyrim (well, maybe not if the graphics were basic.)
If you think of any more of the description, there's a subreddit that's specifically about helping people find obscure games they kinda remember: https://www.reddit.com/r/tipofmyjoystick/
A long shot, but if I think about an arcade game with a barbarian I cannot think about anything but Rastan (although the graphics was not necessarily basic for the time): https://www.youtube.com/watch?v=kFBs3X2LVAc
It’s not necessarily known mainly as a PC game, but the most common 80s game where you play a barbarian with upgradable weapons in Rastan, originally for arcades in the late 80s.
Any ideas?