If the cause is what I think it is, your binding fabric is stretching as you apply it. What helps me is (1) heavily starching the binding fabric before cutting it into strips, (2) not pressing a fold into it before applying, (3) sewing with a regular sewing foot instead of a walking foot, (4) sewing with the binding on top, and (5) sewing on a cutting line I have marked on the quilt with permanent marker and trimming the quilt **after** sewing the binding on.
I know it seems counter-intuitive to not press the binding strip in half before applying, but this actually helps the binding lay smoother. This is because when you go to turn the binding, the outside layer of binding requires a little more fabric and the inside layer of binding requires a little less fabric. This adjustment happens automatically if you have not first pressed your binding strip in half. You just need to be careful at the beginning of sewing to make sure that your binding edges match; just takes a few seconds to hand fold a length to make sure you are starting off right.
Starch stiffens the binding so that the binding fabric is much less likely to stretch as you sew.
Marking the cutting edge (I use a permanent Sharpie) and using the mark as a "virtual" edge helps me a **lot**. I don't have loose backing to get folded under as I sew. Just be very careful not to cut the binding at the corners when you do finally trim the quilt. I decided to trim the corner seams once and ended up with holes in my binding! If I want to trim a corner now, I do that after trimming the entire quilt and then trim away only the quilt sandwich at the corner, not the binding.