Story 1: Legend of Legendary Hero's. The story is basically about a boy who was feared for a dangerous ability. It's not the same as start of weak but he starts of dangerous and uncontrollable. It's a good watch.
Story 2: I can't remember any anime's with this description but there is Zero No Tsukaima which has 4 seasons. It's basically about a 16/17 year old boy who is transported to another world which has none of the technology we use today but is ruled by magic. It turns out he was summoned by a scrubby wizard who made him his follower; this is the first magic spell she has done without blowing shit up. The twist is that this boy turns out to be a legendary warrior. I won't ruin anymore so watch it.