Any cloth will work as a backing and only one layer is needed. There is quite a bit of difference between satin and silk. Silk is a natural fiber(silk moths cocoons) and is stretchy but recovers well. Satin is synthetic. Raw silk can be very strong. I fretted the belly of an osage recurve after I backed it with coarse raw silk.
Once you apply the glue(I prefer Tite-Bond III) it saturates the fibers and the backing becomes homogeneous, cloth, glue and bow back. Silk makes for a strong backing. Pat