Hand history query from the WSOP ME

My question for the hand below - do you ever check back river as MP to avoid getting put in a sticky spot from a good player or is there too much value to be gained from getting a call from a 3 or a 4?

Should clarify - this is a hand from PokerGO coverage (time stamp below) - I am not in hand


9 handed
Blinds 600/1200 BB ante
Day 2 main event time stamp 1:52:24

MP 34,400 A♠︎J♠︎ bets 2500
BB 189, 800 T♣︎5♣︎ calls 1,300
Flop 7♠︎7♣︎3♣︎
BB checks
MP checks
Turn 4♠︎
BB bets 4800
MP calls
River J♥︎
BB checks
MP bets 12, 000
BB folds

You can check back the river in certain situations or vs. certain opponents for sure. Here, the BB has taken the betting lead on the turn, so MP would reasonably expect them to continue betting the river with 7x / 56 / anything better than that-- or anything better than AJ, honestly. (And even a couple of worse hands, like Jx of clubs.)

A value check-raise wouldn't seem to make a lot of sense for BB, since the board except the jack much better hits the BB's range than the PFR's. If BB goes for the check raise, MP is going to check back a lot of the time.

Really MP after taking this line through the hand only bets river with a good Jx or better. ("Better" would be like a QQ-AA that checked the paired board and just called turn for pot control / bluff induction.) Maybe MP bluffs a spade draw with no showdown value, although I wouldn't expect many of those in MP's range-- under 30BB the weaker suited connectors are getting folded pre, certainly from this position.