I would back it if the grain is questionable! You can use silk, linen, rawhide or paper for this, or you can add a wood(hickory, etc) to make it into a backed bow.
Your long string should be as short as possible; loosely strung between the nocks. Once you get out to about 8" on the long string and everything is OK with the tiller you can brace it low, 4" or so, and that will tell you more accurately how close you are; string alignment and limb bend.
If your ultimate weight is 40# you don't want to go over that mark. Try to get everything working as you go out to the 40# mark at your draw weight. Pat