Check back marginal top pairs on wet boards to control the pot, and bluff-catch when the board gets more dangerous.
Checking is the preferred play here. While we have top pair, ATo is a medium-strength holding that benefits from pot control on a board that hits the SB's flatting range well.
Note: Betting ATo here is slightly too thin; checking back protects our range and realizes equity more effectively against a range containing many Ax and spade draws.
We must call the turn lead. Our top pair is too strong to fold to a single bet, even though the 6d completes some straights.
Checking back is the only move. The river 8s completes the flush and several straights, turning our hand into a pure bluff-catcher that cannot bet for value.