I too have limited mobility and space so I manage by finding the center of the backing and placing it on the center of my table. If possible, I tape it down. Then I center quilt top on it, yes before I put batting down. Then I fold one half of the quilt top over and put the center of the batting as close to the middle as possible. I roll the batting up to the center and fold the quilt top back over the batting. Then I fold the other side of the quilt top over and pull the batting to that side. Picture how they change sheets on a bed in the hospital when they can't move the patient. If you are careful and pin as far out from the center as possible, it works. I pin as far in each direction as I can and then I slide the quilt over and finish pinning each side. I always check to make sure I have gotten any folds or tucks in the back before I actually start quilting but with a little practice, it works pretty good.
The reason I do this is my backs have usually been pieced and it is important to have it centered under the top. If your back doesn't have an obvious center, I guess you wouldn't have to do the roll up of the batting and could just put it down after the back like normal.