We should prioritize betting for value with top pair on dry boards rather than checking back and losing potential streets of value.
Checking back is a missed opportunity; we have a massive range advantage and top pair with a strong kicker needs to start extracting value immediately.
Note: Checking back top pair on this dry board is too passive; solver prefers betting small (33% pot) over 70% of the time to get called by 8x, 2x, and pocket pairs.
After checking the flop, we must bet the turn when checked to again. Our hand is still very strong, though the board has become more coordinated.
The King on the river improves us to two pair, making this a clear value bet. We should aim for a larger sizing to capitalize on BB's likely bluff-catchers.