Wonder Under 805 for cotton & it also worked well with that plastic "felt" stuff that JoAnn sells by the bolt. Heat & Bond Lite for wool applique.
Do you window you fusible? Leaving between a scant 1/4" to generous 1/8" frame of the Wonder Under & cutting out the rest of the center usually leaves thing quite lightweight for me.
A couple other options ...
create a turned edge with freezer paper & then pin/glue baste and stitch down. Glues are water soluble so they often soften up after washing or even just with the water used to block the quilt. Wonder Under also will soften a tiny bit when wet for blocking -- though not nearly as much as glue.
Hope that helps! Good luck!