leaning over for too long probably caused you to tweak a muscle. i do this a lot cos i have a sensative lower back. even sitting in a chair for more than an hour makes it stiffen up. i can't see exercise do anything else but help loosen stiff muscles, but if i were you i would try stretching before riding. i don't see saddle height or crank length affecting your back, but it might help to adjust your stem/bars if you can.

i'm in pretty good shape and i don't weigh much, but i tweak it every once and a while where i'm useless for a day or two. that's also cos i'm lifting heavy lights and camera equipement almost daily. i try to do situps and lower back exercises and that helps a lot. you could also try some icey hot or some flexall and see if that helps. it sounds like you're married, so you could also guilt your wife into massaging it for you!