[DJ Sensei]

In your example, OOP, i'd check-fold it, hopefully check it down to showdown. If you were in position, check the turn and value bet the river if checked to.

I think this question is rather similar to "when do I fire a second (or third!?!) barrel?" On draw-heavy boards, I'll be more likely to keep betting. On dry boards like this with an overcard, I'll slow down and probably check-fold. Obviously, NL is a more situational game than limit (simply because the bets vary, and some pots are much more important than others). Because you can be punished much more when behind, and rarely can extract much more when ahead, a more passive play is typically correct in WA/WB situations.