Hey krys, I am 25 weeks along and I am showing a lot, I have got a little tummy now, however I have gained between 5 - 7 lbs so far. I can tell that I am loosing weight in my legs and arms and my face has thinned out. Anyway, about your back hurting, I am not sure about a heating pad, I don't think that it will hurt your back in anyway. I use one on my hips because my hips have been hurting me. I mentioned it to my doc and she didnt' seem to think that it will hurt anything. When I wake in the morning my hips hurt because I sleep on my sides. I do sometimes sleep (if the baby is positioned correctly) with one leg extended all the way out and one knee proped up on a pillow and it keeps them from hurting really badly, but the back and hips are two differnt things. I am also a lot shorter than you are....I am only 5.1 and 130 lbs.
If you are worried about using a heating pad you can call your doc to ease your mind.
Good luck to you, are you haveing a girl or a boy right now?