Tiny’s destiny is depressing. If he signs the Book, he has to die by the hands of a thief who steals his stuff.
Also, according to the fairy tale, the story took place over the course of 5-7 years. If Tiny was born before “Jack” climbed the Beanstalk, he was very young when he lost his father. There’s even a chance he never even met his father (if he was conceived late). Either way, Tiny lost his father “for the sake of the story”.