It may be the needle is too big a gauge, especially with a very light fusible web that doesn't fully fuse the threads (use the 60 or 70 weight sharps). Some invisible threads can cause problems. Polyester by Superior or Sulky is better for that than nylon, which is often heavier and tougher so it pulls, if you really want to use invisible. I've found the bottom line or 100 wt YLI silk looks wonderful...almost invisible and doesn't pull at all. The other thing that can cause that is too loose a weave of the applique material. I have had that happen early in my applique work and ended up using a little liquid stitch (applied with a toothpick or bamboo skewer) to stop the fraying and then I did a visible satin stitch edge covering, which wasn't what I intended at first, but it looked fine and saved my project. If you use the right needle and thread combination, and if your weave is dense enough, you often can get away with really narrow stitch width. If the weave is not dense enough, it helps to widen your stitch. Hope this helps. Cheers, BJ