I spray-baste (holds the quilt sandwich together better, IMO) and I heavily starch the backing fabric before layering. This prevents the backing fabric from stretching out of shape when quilting.
If you don't want to take the sandwich apart at this point, I suggest spray starching both the front and back. Lay out a large flat sheet to catch overspray and lay the sandwich on that. Spray from the outside edge in to minimize overspray, let it dry, and spray maybe twice more. Turn the sandwich over and do the other side the same way. This will stabilize both the top and backing so there will be less stretching as you sew.
How thick is your batting? It's much easier to quilt thin batting than high loft batting.
Also use a walking foot.