I think it's a personal choice, Rita. When I made my first quilt (in the early 60s!!!) I had no instructions, and just folded the backing fabric over the front edges for the binding. It didn't take me long to realize that those thin edges showed wear pretty quickly. If you are making a project that will not be handled much, a single fold might be just fine.
I now use double folds on all my bindings, whether they are cut on the straight of grain, or the cross grain, or the bias, and whether they are piped or not because it's stronger on the part of the quilt that gets the most wear. My quilts are made to be used up and loved to death. Even so, I've replaced bindings on a couple of well loved quilts!
Think about it. Every time you spread a quilt on a bed, or reach to pull up it up snug on a cold night, you will probably be handling the edges. Every time you fold a quilt, you will handle the edges. The weight of the center of the quilt is usually just lying flat on a bed (or body!) without much stress. A show quilt is handled by the edges by the people who hang it and when they fold it to return it to the owner. The rest of the quilt is seldom touched.
Anyone else have pros and cons?