I agree with the recommendations above about how to distribute the weight of the quilt while stitching. I also roll my quilt on each side, then throw the roll over my left shoulder.
I also put my adjustable ironing board to the left of my sewing machine table to give me a place to support the left fuller & heavier side of my quilt.
I take the cover off my ironing board so the quilt slips easily along the surface.
I also put my sewing machine and ironing board on the short side of my sewing machine table so the quilt can stretch out along the longest side of my table as I sew. Literally doing anything to keep it from getting trapped or dragging down either before or after pushing it through the machine.
I also started sewing QAYG so I can quilt each individual patch by itself before joining together. Much less stressful!