Steel doesn't have to be heavy, but some of those old bikes were built to Take It. It depends on the bike.

Have you weighed the steel bike? That will give you an idea of what you are up against. Those old bikes tended to have a lot of Stuff bolted to the frame. Just losing, say, kickstands and fenders is a free "upgrade."

Also, is it running well? Chain lubed? Brakes not rubbing? Wheels true and turning freely and tires pumped? Bottom bracket moving freely? There are other things to look at but that could get you started. Some of those are cheap fixes, and some aren't. It's worth it to check on mechanical condition - again, just so you know what you need to do. Some of those old bikes have lived a rough life. (To be fair, some were babied, too.)

Some easy upgrades would be clipless pedals and faster tires. Couldn't hurt.

Shorter me: I'm a sucker for old steel bikes. I'd be inclined to do what it takes to make it work.