Look and see if you can adjust the pressure of your sewing foot, if so lighten the pressure a little then I always zig-zag the edge so it won't move on me then sew the binding to the back then hand sew the binding down on the front. I also like to do a 3/8" or 1/2" binding since it is easier to control the quilt and I personally think it looks nicer. Also you can put on a wider sewing foot which can help with the drag of the quilt.