I have no experience with double-knit, but I've made a couple of quilts using fleece as the batting. The two recipients both have a lot of trouble staying warm, and they found these quilts to be much lighter than the alternative (e.g., layers of wool blankets).
Because neither fleece nor double-knit shrinks, it's critical to shrink the quilt top, bottom, and binding fabrics as much as possible before sandwiching the quilt. (I strongly encourage you to wash and dry (on hot) the component fabrics before you even cut them.)
I have not found it necessary to increase the width of the binding I use. (I start with 2 1/4" strips.)
I hope this is helpful.