If I had this situation, I would be inclined to do another row of stitching with a short stitch length, just outside my seam line, in the seam allowance. I would then make up a piece of bias tape, lightweight and narrow, and I would first, stitch it on that new stitching line, with the machine, then I would fold it over, encasing the seam allowance and stitch it down, more than likely, by hand, given the fact you have a small seam allowance. You probably could stitch that down by machine, but I would be afraid of one more seam stitching giving more bulk in that area, stiffening it up a bit where you really don’t want stiffness. 🙂
I hope you can save these and get more wear out of them. The fact you said they have been worn lots and washed should make you feel very happy that they have been so well loved. 🙂
Carol