When I bind a Quilt I use a 2.5" strip folded in half then sewn on the front. That folded edge is eventually folded over to the back and secured by hand. The result is a sturdy thick binding (6 layers of fabric actually - plus what ever the quilt is made out of) .
When I bind a runner I use a 1.5" or 1.75" inch strip not folded. I sew it onto the front of the quilt (single thickness) then fold it over to the back. When I sew it in place on the back I fold the raw edge under and hand stitch it in place. The result is a nice thin border (in thickness - it is only 3 layers of fabric) that is sturdy but not bulky. I use this method on runners, placemats and the like that will be used on tables. Because it is less bulky, plates do not usually rock if they are sitting on the binding. The other option is you could also use something like a Single Fold Bias which would give the same results.