I typically avoid c-betting in a situation where I have raised with a mid pair like 88 and get multiple callers, then see a flop like AKx where chances are good that somebody made at least one pair that beats me. I've noticed that a lot of players in the micros will limp-call pre-flop with weak Aces from any position.
If you open in LP with the same type of hand, the BB calls, and there is an Ace or King on the flop, I would almost always c-bet this unless the BB hasn't been defending much. If you do c-bet and a tight BB check-raises you, probably time to fold unless you have a set or better.
In most cases you shouldn't give up on the hand with one opponent just because there is an overcard on the flop, because that makes it less likely that your opponent flopped top pair and you can represent that even if you don't have it.