Do you know the tire size? 700x23, 700x25, 27"x(something)
Wider tires can help, and 80s road bikes often have more clearance for wider tires than modern road bikes. The next issue is wheel strength. I'd say ride what you have for now. You may eventually start breaking spokes. When that happens, buy some 36-spoke wheels from a high-quality builder and they'll last nearly forever.
If your tires are 700x32 or wider, I doubt you'll have an issue with those either.