DisneyFirefly mentioned that you should buy an extra seat, but I have never had that experience. Both myself (size 26/28 womens) and my fiance (size 54/56 mens) are pooh sized, and we ONLY fly Airtran, because we don't have to buy the extra seat required by other airlines. (Stupid Southwest!)
You may want to bring along a seatbelt extender (or ask the flight attendant for one as you board) just in case. Otherwise, your seating should be with the 7yo in the middle. Raise the armrests, and you will be ok.
We have found that if you wear looser pants (i.e. cloth rather than denim), you will have a better experience, as you can adjust easier. With denim, you're body is pretty much staying where it is. Also try buckling the seatbelt before you sit (yes, it's hard, but it can be done), this way the strap is actually laying on your thighs rather than across your abdomen.
Hope this helps, and good luck!