Silk and linen are excellent backings, I have backed some nasty pieces of red oak with silk and made some good shooters out of them.
I like too use the center of a plain sawed 2X for wood backings, and take 2" boards off the sides. I take the 2" boards off the sides first and use what is left for backings. Hickory backings are usually a little over an 1/8" just enough to grind out the saw marks. But I will give a word of warning, if you are ripping with a table saw, the thin backings can remove teeth, a band saw with a good sharp blade is best.