here are my own labels sewn as loops into the inside seam of my burpies:
I fold them over, sew them upside down with a narrow 1/8" seam, stop the machine once I'm "off" the label, fold the label down and back over it, enclosing the raw edge of the tag, and also ensuring that the double stitching secures the label.
Sewing them in this way also lets the label lay flat against the burpie.
The ones in the pic have been washed on HOT and then tumbled dry on HOT before I even cut them apart - they hold up very well.
This also softens the labels a bit, since they can be a little stiff when new.
HTH someone out a bit,