While middle pair is a strong bluff-catcher, it requires careful pot control out of position to avoid being punished by a polarized range.
Checking is the preferred play here. While we have middle pair, betting often isolates us against better 9x and spade draws while folding out hands we dominate.
Note: C-betting middle pair OOP is often a mistake; checking preserves the pot size and allows us to realize equity more effectively.
Checking is mandatory on this turn. The 4h is a dynamic card that completes some straights (A3, 63) and adds new heart draws to the board.
The river 9d is an excellent card for us, but we missed a thin value bet. It pairs the board, reducing the likelihood Villain has a 9, and upgrades us to two pair.
Note: Checking back is a missed opportunity; a small value bet targets weaker pairs and Ace-highs that might feel forced to call.