First of all, I am glad for yuor honest concern. But babies have had quilts are long as quilts have been made. You do not have a make a HUGE quilt for an infant. I am new-born sizes about 30 x 30" -- just enough to lay over them or use in a carrier.
As far as weight? There are good UNFLAMABLE batting to use that are very safe. In doubt? Talk with the Mom and ask her what she thinks.
Julie