When you overbet shove AJ on the turn for value, are there any hands he calls with that you beat? Would he really stack off with TPTK? Otherwise it's sets and a higher 2pr.
What does my hand look like? Hard for me to have an ace, KT I raise the flop with but I probably call with hearts or 9T and peel middle or bottom pair. I might turn the latter into a bluff and I definitely would jam hearts now. If I want to have a bluff jam range I should balance it with at least the top of my value range so that I can credibly rep a good hand but don't need to be dead-on right with a hand like A7 that he'll call w/Qx for the value jam to be right. Keep in mind that my range is very polarized as I'm unlikely to have just Ax.
Also, when he checks, I expect him to have either nothing (not giving me action anyway) or a bluff-catcher as most people bluff that ace so if he had a big hand he'd bet to get a suspicious look up (especially since it's hard for that ace to hit me). Way to get him to call with a bluff-catcher is by jamming imo