We turned a pair and rivered trips, but on a board where the most obvious draws completed, we must be cautious of a check-raise.
Checking is the preferred play here. While we have a gutshot and an overcard, our hand has decent showdown value and benefits from realizing its equity for free.
Note: C-betting is fine but checking is higher frequency; our hand is a great candidate to check-back to protect our range and realize equity.
We turn second pair and still have our gutshot. Betting is the primary recommendation to get value from flush draws and worse pairs.
Note: Checking back misses a value/protection bet against the BB's wide range of draws and smaller pairs.
Rivering trips is a massive improvement, but the board is quite dangerous. Checking back is a very viable trap or pot-control line.
Facing a check-raise on this specific runout is a nightmare. While we have trips, the BB's line is extremely polarized toward straights and full houses.
Note: Calling the raise is risky; on a board where A4 and 64 are very possible, trips with a weak kicker often becomes a bluff-catcher.