I think that you played well preflop. About the flop I really don't know why the villain check, it's confusing for me.
The moves that he made looks like he has AK, re-raise about 3xCOraise preflop, and then check on the flop. That's my first guess, and the other is that maybe the villain has QQ+ or TT and waiting you.
I don't know, I think that the lot of this will depend about the next move of the villain. If he raise you go fold, and if he only call then everything will depend about the turn and about his move on the turn. If he raise more than $1, go fold, and if he again go check and it will be dealt lower card than Q, then bet to $1.