Chicken men? I like the term lightbulbs.
Here's what I do for back. I work-out twice a week. At least once a week, I do my back work-out. If during my second work-out, my back feels completely recovered, I'll do my back in my second work-out for the week. In other words, play it by feel rather than by schedule. I do this, because I've found that while I make less progress than doing it every work-out, taking it easy on upper back exercises is important since it's easy to hurt your lower back.
As to what exercises, my arms are so weak, I've never felt pullups or rows work my back at all. Pullovers (lay w/ back on bench, hold a db with both hands, keep arms straight, and pull weight upwards using back muscles) used to work my back some, and seem to help w/ depth, but they haven't helped in a long time. About 30 years ago, I ended-up strong enough so that it took so much weight on that excercise that it hurts my lower back and elbows to try to hold the weight. With my build, deadlifts are almost 100% a lower back work-out and 0% legs. So, I work lower back hard, and I simply can't work-out my upper back. Sorry, can't help you with suggestions for what in particular to do.
Weak back? Are your shoulders rolled forward from the imbalance? When I first started lifting (about 40 years ago), I saw a lot of guys that had the problem. Most of them did only bench and no back exercises. Also, most of them developed shoulder problems, and it just looked funny. So, work-out those posterior deltoids to help keep your shoulders back and to help prevent injuries.z