[adanthar]

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He could (and, in point of fact, did) have a pocket pair, so flopping an overpair wouldn't help, and even flopping an open-ender leaves me as a dog. I think trying to put him on a specific hand (he has an ace or he doesn't have an ace here) is futile, especially online. Again, if I am planning to fold most flops, I should have folded preflop (which is now starting to seem was the right thing to do).

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With 10xBB, and the big stack having limped in, let's give him the typical AA-99, AK-AJ range. You can modify it down a fair bit without changing these numbers; they're just an example, but it should give you an idea.

With that range he has a big ace a little over 50% and pairs the rest of the time. If you flop an overpair/draw, sometimes you'll push and he'll have to fold his AK or, at least, you'll have 6 or 10 outs. So calling for a set or pair+draw/overpair type flop makes sense given implied odds.

Once you get here, though, the calculation is straightforward. Over half the time, he has an ace, and some of the rest, he will call anyway. You are betting 1400 to win 1500. Is this gonna work enough? No? OK, check/fold.