What a find! I can relate to how heavy it must be. I would probably not put a batting in it, unless very thin. I would probably use a bit more quilting as the weight of the squares when pulled or tugged( if you use it as a bed quilt) to reposition the quilt can couse the seaming threads to give. Quilting a bit closer will help that issue. Quilting it will also help some of the sag if you choose to hang it. Use a universal needle or ball point needle when quilting and I would increase the lenght of the stitch to a 3.0 or 3.5 .
Back it in what ever suits your fancy! If you use it as a bed quilt it will be one of the warmest quilts! ALL that poly and all those seam allowances will certainly keep you warm .. and probably from moving around to much under the weight.