I've used a thin poly batting and also flannel in a number of baby quilts for my grandchildren and found their weight fine. All were bound as usual. **Do Not** use steam-a-seam. Fleece is a plastic product and will flatten and probably melt with the heat of an iron.
I always use a few dabs of fabric glue, instead of pins, to hold the label in place then sew it on using either a tiny whip stitch or small blanket stitch.
ellie