We should check-call with our marginal top pair to protect our range and catch bluffs rather than betting into a condensed range.
Checking is the preferred play here. While we have top pair, our kicker is weak and betting often isolates us against better Ax or strong draws while folding out hands we dominate.
Note: Betting here is too thin; checking protects our range and allows Villain to bluff with their air.
Once we bet and face a raise, we are priced in to call. We have top pair and a backdoor nut flush draw, giving us enough equity against a range of sets, two pairs, and spade draws.
Checking is mandatory. The board pairing the deuce is generally better for our range, but we need to control the pot with our marginal two pair.
We must call this small turn bet. Our hand has improved to two pair on a paired board, and the price offered is too good to fold.
Checking the river is standard. We are out of position with a hand that has showdown value but cannot comfortably bet for value against a range that contains full houses.
This is a very tough spot, but calling is justified by the pot odds and the fact that we don't block the missed spade draws.