When embroidering thin and stretchy materials, one cannot overestimate the importance of stabilizer. With a properly digitized small design, you should only need to use a single piece to get a clean look.
When selecting stabilizer, you’ll want one that doesn’t stretch, shrink when washed, or lose integrity during stitching. Remember that thin materials also suffer from show-through. A standard wet-laid cutaway backing has what we need, but the thick, cardstock-like backing leaves hard-edged silhouettes around designs with even the best trimming, and its girth can weigh down and distort thin materials when worn. This tempts us to use tearaway for more complete removal, but this can become less stable the more it is stitched, which makes it a less than ideal choice.
The act of tearing away the excess can also cause damage to thin materials through stretching. This in turn increases puckering, or can lead to small holes or tears at stress points in the design unless handled with extreme care.
A cutaway polymesh stabilizer provides both dimensional stability and omits the heavy edge of a standard cutaway. For materials that will be viewed on both sides and/or are see-through, a thick, fibrous water-soluble backing can be used to provide stability during stitching and complete removability.