Check or bet turn with effective nuts

Question

I was playing a hand at the casino the other day and I made a decision that I am not too sure about, let me know your thoughts.

CO has about 60bb behind, I have about 120bb, sb covers me

Preflop action: I am in the big blind with 9♠9♥, cutoff opens to 5bb, sb calls I elect to call.

Flop 9♣7♥7♦

sb checks, I check, CO bets 11bb sb calls I call

Turn 3♠

sb checks, I check, CO bets 21bb sb calls I call

River 4♦

sb checks, I check, CO checks and shows A7o, sb mucks.

I am wondering if checking is the right play on the river, my thinking was that if the CO was going to bet flop and turn on a relatively dry board they are very likely to have a seven and maybe a strong 9 (although I block 9's). I definitely think it was a mistake on the part of the CO to not bet this river, given the action up until then and how strong their holding was. I decided not to 3-bet this hand preflop to close out the action and keep hands weaker than mine in play, as the CO especially tended to raise a weaker range during this session especially from later positions. My reasoning for checking the river in the moment was to encourage the CO to bet again with a 7 or the case 9 so I could raise all in. Given the CO's hand, a min raise on the turn or flop most likely would have been called by him but I wanted to keep both the CO and SB in the pot so I elected to call in both spots.

Answer 1

Preflop: fine defend. Might put in a 3bet squeeze once in a while if stacks were deeper. Should be concerned about SB's range given that he cold called and has to play OOP to two players.

Flop: good call. At this point, try to assign a range to both players that would play this way. It's easier to think about SB's range as his cold call range preflop should be rather tight -- here I would assume SB has A7s-AJs, 77-TT, JJ maybe (since it would more likely be 3bet pre), and definitely not QQ-AA, then some suited connectors or one-gappers that have backdoor flush draw or straight draws (stuff like 87s or T8s). CO has a range slightly wider than the SB since he is the preflop aggressor, and should have all pairs 55-AA (maybe even 44, 33, or even 22, depending on how tight of a player her is), AK, JTs, etc.

Turn: when CO bets half his stack here, he is likely willing to put the rest of it in on this street if he gets raised. You beat most of these hands (any overpair, any 7 except for 77). If he folds to a raise, you weren't going to get any more from him on the river anyway. The concern now is trying to get SB to commit stacks, and you can only do that with a raise. With this board and specifically this turn card, it is very difficult for any one player to improve to a good second place hand on the river. If you just call here, most rivers will check all the way through, since you block your opponents from having anything good.

River: since you missed value on the turn, I think the only way to get called is to polarize your hand and rely on your opponents to make the mistake and call. I would get anywhere between 90%-120% of the pot here, since the only draw that gets there is 65 (double gutter on the turn).