AK ip vs limp

On the turn, he should have something to bet/ call you.
On the river, bet sizing is really weird and it should represent monster. As palyed I just call the river on that paired board.

Against this fish just go big preflop. I would 4bet/stack off preflop 100% of the times here.

Flop - raise the flop. You hit top pair top kicker in a 3bet pot vs fish who cbets 1/5. No need to follow gto or fancy calls here. There is 1 hand that beats you. If he has AA - cooler. Try to get it in vs his weaker hands and do not let him draw cheap with hands like JT, QJ, QT, etc. The fish will call off all these.

Turn - you finally decide to raise and get called - so he must have a piece of the board. I would raise a lot bigger though - to 1.30 at least.

River is just a call - J improves his range (if he has any as he is a fish) and i dont think a weaker hand is calling your raise. Spare yourself the last 34 big blinds by folding to his reshove - you are never good there. Yes you need to win a very small percentage for your river call to be profitable but in reality you are winning 0% in this spot. The fish will not overshove with J9 and KQ which are the only hands you beat

it seems you played the hand like you are playing vs reg - you flat preflop, you flat the flop, etc etc while in fact you have a huge range advantage vs the fish. These are the spots where you make money in the long run. Not spots like KK/AA preflop vs the regs.

Yes, river raises like this are usually very strong, so most of the time you are rarely ahead.