The cotton Quilter's Dream batting that I used, which made stiff quilts, was the lightest weight (and the thinnest). The most drapey quilts that I've made were with thin 100% polyester batting. I think the key is air spce between the fibers...the more air space, the drapier the finished quilt.
Not much air space between the cotton fibers in Quilter's Dream batting, but lots if air space in the some of the lightweight poly battings.
Personally, I'm not usually a fan of the poly battings, because they are difficult to machine quilt...no body, so they flop around as I try to quilt them. I like the firm feel of the cotton battings, for my wall quilts. Not trying to convert anyone here...just sharing my experience and preferences.