So, I went over and took the belay class at Planet Granite over in Sunnyvale today. I learned useful things like how to tie a rope to your climbing harness so that you don't go splat, how to handle a rope so that your climbing partner doesn't go splat, and I got to do a bit of climbing.
Climbing was interesting. It took a little while to get over the sheer adrenaline rush of, "I'm up a wall hanging off some teeny little hand and footholds!" I can tell that if I want to improve, I'm going to need to get a bit more willing to fall - intellectually, I've got complete faith that my belaying partner can catch me, but the hind brain is still going, "Gravity! Shiiiit!"
I think the strength I've been building through weightlifting served me well, although I still found a short climb surprisingly taxing. Although some of that was probably due to my tendency to take a death grip on my handholds while my brain was trying to cope with the whole falling thing.
Anyway, assuming I go back and pass the certification test (which really shouldn't be a problem), I'll be a qualified belayer, if any of my friends who climb need one.