I don't think it will stretch the string, but it WILL damage it. Hanging in one positon like that will "dent' the string and weaken the fibers where it's hanging. Your better bet would be to take a 2 x 4 or something similar and make a rack of sorts. Like you would see at a pro shop. Drill a hole in it and insert a 3/4 or 1" dowel rod. Hang the bow from that. I wouldn't use hooks on the string.