A thin layer of fiberglass cloth wouldn't compress the belly. It'll work. But I gotta ask why you are doing it.
There are better choices for protecting the back from raising a splinter. Rawhide or silk would be my choices.
If you want the backing to do some work, sinew is a better choice. I am sure you know that it wouldn't be a selfbow then. It would be backed or composite bow.
Glass backing is counterintuitive to the purpose of using wood for a bow if you ask me. It is difficult, messy, synthetic and stinks.