It could simply be dried grease. Headsets don't magically tighten, so the likeliest suspects are dry grease or rust.

Following the theory of trying the simplest remedy first, turn the bike over and apply a few drops of oil to the gap between the bearings. Swing the bars back and forth to draw it in, and continue to do that to circulate it and work it into the dried grease. If things begin to loosen and feel more free, we're on the right track, and a bit more time will soften the grease and restore to nearer to new condition.

Of course adjustment may be needed, but in almost all cases old bikes have headsets that are loose rather than tight.
Also know that the single most common cause of tight headsets (other than lube) is a fork that's bent back slightly, usually from a front end collision. So if it isn't dried grease or rust, sight down the handlebar stem, headtube and upper end of the fork blades like a ***** and verify that all are in line. (IMO, this is the first check to be done on any used bike).

BTW- if, as you ride, redish/brown oil or grease weeps out of the bearing, then there was some rust, but if it feels good and steers well you're good until you're ready to do a proper service on the headset.