He overplayed his JJ, that min raise is weak. If he wants get the pot now he should have pushed. His min raise gets him no info on what you are playin. If he is worried about AA or KK this bet gets him nothing. A lot of players would smooth call his raise with AA or KK and think that they can get all his money after the flop.
Your play, well to say you hit your flop is an understatement. I would have folded to the
$160 raise why? Because you dont want to be in this hand, by calling you are building a huge pot, you dont want to play a huge pot with 36s. The problem here is what happens if you flop a pair and say a gutshot straight draw now you are tempted to call another bet for pot odds. You are growing the pot even more and most likely your at least a 2:1 underdog.
Nice pot though. I bet your opponant was pissed when you turned over 3/6.