When you are looking at the Hobbs website, check out their Thermore batting. It is thin. I believe that original crazy quilts did not have batting, and they were not quilted, but instead tied.
My parents received a crazy quilt from my grandmother for their wedding. It was not the delicate silk kind, but was made of wool suitings and heavy cottons. The batting looked like feed sack, and the backing was heavy. It had nice embroidery and was tied. It was made specifically for the cold ND winters and greatly appreciated by my parents, since their first apartment had very little insulation.
You can make yours any way that you like.