Hand 1: I go to calldown mode. If he really had the jack, I think he'd be tempted to check-raise the turn. I think he has a seven and thinks with two jacks out you don't have anything.

Hand 2: I'd bet out the flop hoping to get raised by preflop raiser since that ace hit. Then we can 3-bet the flop and he might cap. Then you fold on the turn? Button could be betting a flush draw that came in since he called both bets on flop. Again, I lead the turn, if I get raised, its three bet time again.