Continuation betting a lone calling station

[Xhad]

Lately it seems that I've been running into a lot of people that fall into the following pattern if heads-up or shorthanded:

-They will limp/call from an early position, or defend their big blind with almost anything
-Any hand they called with preflop they will call almost any flop
-They will fold on the turn if they still have nothing
-They will generally not bluff the turn even though you checked behind on the flop
-They may be clever enough to c/r the flop, but they won't check a good hand the second time if you checked the flop
-They are not clever enough to realize that you might have checked the flop because you missed, then bet the turn because they checked, and will still check/fold the turn even if it "should" be obvious you don't have much.

I realize that is a LOT of "if"s but it seems every online table and most B&M tables I've been playing at lately have at least one player that fits most or all of these.

So...what I'm wondering here is what conditions need to be true to cbet on the flop? Do you need a pair? Overcards? A reasonable draw? This is all under the assumption that you will nearly always be called, and betting the flop has little to do with your fold equity on the turn. Does flop betting even AKo make sense in this situation?

I haven't heard any discussion of the PFR/check/bet line anywhere, but I'm sure I'm not the first to think of it. Is there something I'm missing? Or am I just overestimating how often this comes up?

Thoughts appreciated.