TPTK vs odd river raise

you are so rarely ahead here... The raise makes no sense but you will see

a lot of 2x , TT and 77 there
and occasionally AK and rarely AQ maybe

Agree. But I also would have chosen a different line. I would have bet on the flop with a Ace high and backdoor flushdraw. He could have sensed weakness in your game and maybe he is not a good player and put you on QQ or KK and tries to put you off of the hand. Otherwise, I think indeed you are behind so a fold would make sense here.

I would also fold here. You should have way more information on him to know if he can bluff you here with air or smth. In general this is just a slowplay.

In general I don't like betting such flops with AK, because I'm too weak for a value bet and too strong for a bluff. To put it another way, I expect to be slightly ahead against the villain's range, but when I bet he only calls with better hands.

I agree totally with the fold here. Not much we can beat or split with and a bunch pf slowplayed better hands.

I like your line, no reason to get the flop. As thazar says, the raise doesn't make sense but you're rarely ahead. Fold to his raise.

I'd cbet around 1/3 on the flop because he'll call a bunch of bad hands and we have tons of backdoors. You can proceed by bet check call based on size on rags or bet any heart, AK, Q. And check back without the backdoor fd.
RIVER
Doubt Ax folds to psb here when it's paired, but random pocket pairs, K highs should fold to your size, maybe even Tx will some.

So I'd bet close to pot, target Ax or bet around 30% target his whole high card+ range on the river

And fold to a raise this size, you just rarely see a bluff here.

Just one note on villain's line. Actually makes perfect sense to play his strong hands like this and this is because when hero checkbacks this kind of board, very frequently he will have Ax or some very trashy hands, so after the flop goes x/x and an A rolls out on the turn, villain can expect hero to bet turn + river very frequently either with his Ax and plus some bluffs, so it's better to keep checking strong hands. and go for the river x/raise.

edit: This way villain protects a little bit his range, but since still don't have enough strong hands to slowplay, hero can value bet two streets with his Ax hands. ( hero can go for bigger bets btw ).

Yeah, I agree with the fold too. I don't agree with not c-betting though... Sure we're often ahead, but any hand has at least 6 outs against us, plus besides our outs against small pairs, we can double barrel any J, Q and hearts, so that's 24cards we're barreling, right? 4 J's, 4 Q's, 3 K's, 3 A's, 10 s. So I always c-bet such a situation. AND we get valeu from club draws =P