yeh this is bad, i would be trying to get to showdwon when he min raises the flop.,
Pre flop I put him on the following range that may raise this flop
Board:

Dead:
equity win tie pots won pots tied
Hand 0: 26.815% 24.60% 02.21% 11935 1073.00 { AcQd }
Hand 1: 73.185% 70.97% 02.21% 34429 1073.00 { JJ-99, KTs+, QTs+, JTs, T9s, KQo, QJo, JTo }
Now this is his calling range when you shove
edit: i put 10x in mre than jx but it doesnt make difference
Board:

Dead:
equity win tie pots won pots tied
Hand 0: 22.792% 22.24% 00.55% 7047 173.50 { AcQd }
Hand 1: 77.208% 76.66% 00.55% 24286 173.50 { JJ-99, KQs, JTs, T9s, KQo, JTo }
Basically getting it in on these kind of boards vs alot of guys who peel in position is going to be a huge mistake, if we have

vs alot of players I just c/f, but because we do have decent equity and perhaps the best hand and want to keep initiative I think b/f is best on this occasion, when he does min raise, I call and c/f close to 100% of turns to "normal" bets and continue to any stupid small bet.