[Dale Dough]

I don't think it's as clear-cut as everyone seems to be saying; who the [censored] plays AJ or 77 like this? On the flop, if I were him I would be like 'I'll try to build a pot now, because the hand that's most likely to pay me off is a (weaker) jack. If any eight or higher comes off, either he improves his hand to beat me, or he has one more hand to worry about and is less likely to give me action'. J8 OTOH seems like a go for pot control on the flop type of hand.

Of course, he could have eights as well, and/or just be retarded (I didn't / don't know exactly how to do the math, but even eights probably is an iffy four-bet). Assuming of course you didn't have an extensive bluffing history vs. each other.

Rereading the OP 'bets strong with big hands' only enforces the notion in my mind that he should have been more aggro on the flop with hands that you beat.

In the end, though, I'd probably still push and hope he has 88 and thinks you got married to your AJ. I think the quicker the pace of your little raising war, the better for you. I mean I'm sure he's no dummy but you did say he limp-calls every hand. As you know it's 50-50, so the only assumption you need is that he'd play 88 this way. It would definitely help if you've seen him check-call mid pair-ish hands on the flop before, and underestimate the significance of one more raise/reraise.

Whatever you do, you can't just call, though - any 7 or higher is a bad river card for you and the rest doesn't change anything.