[VoraciousReader]

Full disclosure: I read the thread this before replying. I'm surprised I remembered how.

This is actually one of the situations where I am working on NOT auto-betting the flop after I raise. I think several factors here argue against a flop bet:

1. You have only 1 overcard to the flop, and there's a decent chance someone hit the high card. People like to play kings.

2. You are at a table full of loose passives, who are probably seeing at LEAST the turn.

3. You are betting into a field of 3.

4. You are out of position. I might fire a bet if I were acting last and all had checked.

When I bet a flop like this in this situation, it usually goes:

flop: I bet, all call.
turn: I bet, 2 call, 1 folds.
river: I check (or spew one last bet), others check or call.

One player has pair of 7s/pair of fives/or pair of kings with a 2 kicker. I lose. Third party has something random like 10h8d. This has actually been a big leak of mine. I think you played it well. But if I were at a tight table, or on the button, or the top card were a jack, I would play it differently.