a lightweight non-woven fusable stablizer will fit your needs- at stores like joannes, hobby lobby, other fabric stores (not all quilt shops carry stablizer- they carry paper backed fusables for applique)
the stablizer is white- has fusable on one side only (feels like little bumps on one side) you press the stablizer onto the back of the fabrics- then cut them out- they keep everything nice and straight. it is light weight - but it does add an extra layer to your quilt- so machine quilting will be recommended- it's hard to hand stitch through all the layers.