Bet overcards against single opponent who c/r.

[f97tosc]

I am a newbie playing 2/4 B&M. Things are going very well following SSHE closely; usually most or all players are extremely fishy so it doesn't take much. Recently I have been moving up to 4/8. Sometimes the players there are just as bad, but sometimes there are a couple of players who are pretty good, at least compared to me.

Now to the question. Even if I raise preflop in 2/4, I usually have a several callers, and so if I miss the flop I move on as I would with a weak drawing hand, as per the overcards section in SSHE. I would like to think that I do this well.

However, in my last 4/8 game I raised with AKo preflop and was left with a single player, one of the better ones. I missed the semi-structured flop, he checked to me, I bet, and he checkraised. In the unlikely event that this would have ever transpired at my typical 2/4 game, I think I could safely have thrown my hand away, since that crowd rarely c-r and when they do it always signifies a strong hand. But now I wasn't so sure, what if he was bluffing or semi-bluffing? From a meta-game perspective, if I always threw away my hand here, it would seem like he would have a very profitable play by always checkraising my bet. So what should my line be here, on the flop and onwards (if I don't fold)? Or was it wrong to bet in the first place?