I prefer checking the flop, betting turn (or calling turn if V leads), and evaluating river (most likely betting if checked to, calling if V leads). This is a medium-strength hand in a 3! pot. I don't want to play for stacks. It's good to have top pair in your check back range once in a while so Vs can't automatically put you on whiffed overcards or a smaller pair.
Also, against this player, once he calls the 3! his range should be much stronger. (You did say he folded to 3! a lot previously. Unless he's fed up with it, he should have a decent hand.) So we beat QJs, JTs, 88-TT, losing to AJ, 77, JJ-QQ. We're exactly not a huge favorite against this range. A bet isn't bad, but I just don't see getting called by worse over three streets unless I think this V can make some pretty horrific call downs with JT/QJ.
I used to 3! these offsuit broadways on occasion, but it usually bit me in the a** as I'd run into the top of Vs' ranges and get owned. Don't bother anymore, I just fold.
Last edited by DumbosTrunk; 01-02-2019 at 05:08 PM.