Hide glue is what you want. I have used Knox gelatin from the grocery store on a couple-three with good results, it's just finely refined hide glue. And yes, the sinew backing will add considerably to your draw weight.
Be sure to degrease the back of the bow good before you start gluing the sinew on. Sinew backing is a lot of work and a very messy process, but it makes a good bow. The only gripe I have with sinew-backed bows is trying to keep them from soaking up too much moisture and turning into wet noodles here in the humid southeast.
Yea, mix 3 envelopes of Knox unflavored gelatin with a half cup of cold water, bring it to a boil and let it cool a little, and you just made a batch of hoof glue.