It occurs to me that I might exercise more frequently if I could do it just as effectively without weights, simply because then I'd be able to do it at home or when I was out of town.
I was about to solicit routines here (for strength-building without weights), but I figured I might as well provide my own links I found first.
If anyone has the time, let me know what you think of the advice given at these links, and even better, let me know whether you have other suggestions.
Or tell me whether you think it's really not possible to replace weights. If it makes a difference, my personal goals are just to lose a little weight, maintain some decent tone and get stronger for the purpose of avoiding injuries. Getting bigger is not important to me.
Visualized Resistance Training
Suggestions from Fighting Arts forum
Paul Becker suggestions
Lee Haney suggestions