Folding small overpairs in spots like these is at worst a small mistake.
In the specific original scenario, calling to evaluate the turn is probably fine.
1) Villain is a bad LAG/good LAG/weak tight/loose passive/good TAG/nit.
2) You have a nitty/TAG/LAG image.
3) You have 200bb or 70bb stacks. Why does this change your play (if at all)?
4) The flop is 842/J42/QQ5/etc
5) This is 10nl/100nl/1000nl/etc.
6) Villain pots the flop.
7) Villain checks the flop
8) Villain has position.
9) You raised from UTG/BTN.
10) If you raise, what are you doing against a call or shove?
11) If you call, what are you doing against a lead on various turn cards? What are you doing if he checks various turns?
12) What if you have 67s or AK here? How and why does your play change?
13) Most important, why does your play change with the different variables?
1) Against certain bad LAGs, I call the flop. Against a good LAG, I fold the flop. Against a weak-tight, I call or raise. Against a loose-passive, I fold. Against a good TAG, I fold. Against a nit, I fold.
2) If I'm playing LAG and they're aware of it, I realize that their range might be slightly wider. That said, I'm not sure that it has a big enough effect on my decision to alter my action. Certainly not as much as the first point.
3) With 200bb stacks, we can more easily call the flop and evaluate the turn. That said, we're also potentially going to be facing a lot more pressure on all streets. (Though our opponent may face that same pressure.) With 70bb stacks, our calling pre-flop is a lot closer...but I think I'm default folding (maybe calling) there also.
4) Flops are pretty similar...though I'm more hesitant to fold the 3rd one since it's the only one that might reasonably cause a better villain hand to slow down on later streets.
5) Limits shouldn't affect anything aside from the general quality of opponents...in that regard, see the first point.
6) This typically makes me think that villain has less of a hand since he's betting so large on such a dry board. That said, it may just be the player's standard bet. If I do think it's weakness, I prefer raise/folding.
7) I bet here and cry when the villain decided to get cute by check-raising his bigger pair. (That said...it does pick up the pot a lot from someone that whiffed AQ/AJ and decided to shut down.)
8) Villain having position makes me even more reluctant to continue.
9) If I raise UTG, I expect any competent villain to give me more credit...and thus show up with a narrower range...which inclines me to fold. If I'm on the button, he could be playing back a bit wider, so that inclines me a bit more to continuing.
10) Folding typically. Villain will've said he has a better hand 3 times by that point.
11) The reason this hand is such a pain is that even if we're not beat now, there are 20 cards that can come on the turn that could connect with villain's overcards, so we're going to be somewhat blind in that regard. The only saving grace is that we've got position...but we're almost never winning this pot by knocking villain off of a better hand than ours.
12) Unless I have a specific read of villain, I'm folding those too.
13) I think I've justified each, but I can explain more if you'd like.
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