This is the end of the story. If you haven't already read the set-up to the situation, and want to do that first, see here.
It's $102 more to call. Including my flop bet and his all-in, there's $216 in the pot. It will cost me $102 to win $216, which means that I break even on a call if I can win the hand about 47% of the time. [EDIT: Should be 32%. See comments.] More than that and it's profitable to call, less than that and it's not.
After the hand was over, I texted Donna that I had had A-Q. She responded, "What range did you put him on?" That, of course, is exactly the right question.
The problem was that he would likely consider his pre-flop playable range to be quite broad, since he had the button, the raise was not large, and there were several limpers, all of which means that he was getting attractive pot odds to play some oddball hands. I might ordinarily discount two-pair hands here (Q-8, Q-4, and 8-4), because people tend to fold those to early-position raises. But if he had them suited, he might well have deemed it worth seeing a flop, given the small raise, callers before him, and position. Of course he could have pocket 4s or 8s for a set and push rather than slow-play because he didn't want anybody hitting a flush. In my best-case scenario, he would have a queen with a worse kicker (Q-K or Q-J, especially), or a lower pocket pair (9-9 or 10-10, say), and just not believe that my continuation bet meant any real strength (especially if he had noticed and remembered that this was my third c-bet in a fairly short span of time). He might have A-Q for a likely chopped pot. He might have just a flush draw, and, if so, it could easily be the nut flush draw with suited ace-baby, in which case he would think (wrongly) that he also had ace outs in addition to club outs, even if he put me on a queen. Finally, he could have some combination--pair and a flush draw, or flush draw plus a gutshot straight draw. Big pairs (A-A, K-K, and Q-Q) seemed unlikely, as I think he would have reraised pre-flop in order to thin the field. Maybe he wouldn't have done so with Q-Q, but that was statistically very improbable since I had one in my hand and there was another on the flop.
In short, it was a vast array of possibilities. I felt confident that he wasn't on a pure bluff, but that was about all that I could definitely rule out.
As far as physical reads, my impression was that his hesitation was a fake, an attempt to look weaker and more indecisive than he really was. But I didn't put much confidence in that, since I had seen him play so few hands.
I thought about it for a minute or so. My sense was that the number of hands he could have in which he was already ahead, plus the decent equity he had with his drawing hands put my chances of winning below 50%. On that basis, I finally folded. But it was a close decision. If it would have cost me, say, just $60 or $70 more, instead of $102, I think I would have gone the other way on it and called him.
I had two other general considerations. First, I think it is usually wrong to play a big pot with just one pair, even if it is TPTK, especially when calling rather than being the aggressor.
Second, whenever I open-raise from early position, I am deliberately raising smaller than I would in late position because I don't want to play big pots from bad position. When doing so, I always remind myself of exactly that, and get it set in my mind that I will need to be more inclined to fold than I would be with the same cards in more favorable circumstances. (I discussed my pre-flop raising strategy and formula in some detail here.)
In fact, there's a decent argument to be made that A-Qo is not strong enough to play for a raise from such early position, and limping with it isn't great, either, so it's best to just throw it away and avoid the difficult decisions and costly blunders into which it can lead you. As Tommy Angelo memorably phrased it in Elements of Poker (page 179), "To me, the early positions look like a desert wasteland. It's a place where people die from overexposure. Which cards do I play from positional hell? The ones that can take the heat." A-Q can't take much heat.
After looking it over through the retrospectoscope, I think it's a very close decision, and it would not be too much of a mathematical mistake to go with either a call or a fold.
I'll confess to one other factor that made me lean towards a fold: It was getting late, I was tired, and I knew I'd be leaving soon. The night before, when entering results into my spreadsheet, I had happened to notice that I had scored six consecutive winning sessions, all of them between $100 and $300. If I folded my A-Q, I'd still leave with a profit of over $100 on the night, and that would extend the streak to seven, which would feel nice. If I called and lost, I might not be able to get back across that $100 threshold before leaving--or, worse, I might keep playing after my A-game had slipped away in a silly attempt to continue the streak, and really blow it. I fully acknowledge that that is an utterly absurd and irrational consideration, a factor that should never enter into the decision. But sometimes it just does, despite my efforts to whip into submission my remnants of irrationality.
I'm comfortable with my decision to let it go, but I'll never know whether it was correct in Sklansky bucks, because my opponent didn't show his cards before passing them back to the dealer. Sorry to disappoint you with no definitive ending to the story, but that's how poker usually is--it leaves you hanging, wondering whether you did the right thing.