AK Deep

[DJ Sensei]

The hand that jumps out at me for villain is JJ. Strong enough to raise your pot-sized lead after a PFR, but not strong enough to push against your 3-bet when you could have AA or KK. You could be against AK/AQ/AJ also, but I don't think any of these (aside from AK) will call your push. QT is out of the question (probably) based on calling preflop and not 4-betting the flop.

Basically, by pushing you chase off the hands that you beat, and get called by the ones you are behind or split with. I'd recommend a bet for 1/2 the pot or so (fold to a raise). If you are ahead, you'll still get called. If not, its no different than before. Then, you can get the rest in on the river.