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This is such a great example of why you need to know your opponents. I agree with the poster who said that given the percentage of the effective stack that already went in, if you think the hand is a good play, put him in preflop, and if you don't, fold it. With 1/3 of his stack in preflop, and first to speak, he has an easy push with anything. The flop and bet that actually happened are the second-best example; the best would be a total rag flop, where the best hand going in is still the best, so you're still betting you have the best two-card hand just as you were preflop.
It's similar to deciding when to play back against a continuation bet.
You paid for information by reraising (although that wasn't the primary reason for the 3-bet), and against a tight player you probably wouldn't think twice about tossing AJ to a 4-bet; but you already said you expected LAG behavior, so this is probably a good spot to out-LAG the guy.
I agree the situation on the flop isn't too good. You'd have to call 42% of the total pot when you probably have about 36% chance to win, under slightly charitable assumptions. You're probably drawing super-thin more often than he's bluffing, too. If you were going to be playing this guy a lot in the future, looking him up here might be worth something later, but that isn't too likely in μ-NL.
Oh, and .02/.04 online NLHE may not be the best testbed for developing reads. I'm a regular microlimit player, and I don't go that low even with a short bankroll precisely because there are too many ATC players, so you rarely know what's happening in a hand.
As a post-post-script, I hate AJ off. In general, I'd rather have coordinated babies or something.
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