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(this is my first strategy post, so I hope I don't suck!)...
I'd like to ask OP, do you have a HUD? If you answered it somewhere, I missed it. I've just started reading FTR again and the last batch of hands are ones that you have posted. But, without detailed reads or stats, the advice you receive is just not as accurate. As several people have said, you are at a huge disadvantage w/o some hand tracking software. And, it's not just for the HUD, it's immensely helpful in analyzing your own play later.
If you don't have a HUD, then my advice would be to play just 1 or 2 tables and take HUGE amounts of notes until you build up a useful profile on the players you play against regularly. And, even if you do have a HUD, still take tons of notes.
If you do have a HUD...
You say you don't have much hand data but VPIP/PFR converge into useful stats pretty quickly. In this hand, his fold to cbet is critical. Floating seems to be the new black right now and I come across so many regs who are folding to cbets less 40%. So, you look at that number (given enough hands to make it useful) and if it is a more standard 65-70%, then you cbet this flop. If he calls, you shrug your shoulders and check/fold unless you hit your cards.
BUT...a lot of floaters will have low "fold to flop cbet stats" but normal "fold to turn cbet stats". In that case, follow Openside's advice and double barrel.
Having said all that, this isn't a great flop for you and C/F'ing is certainly a safe option. Again, having a read on the villain's range is critical.
One more question: What is your normal cbet size, especially in 3 bet pots. If you are betting 1/2 with air and 2/3 or more when you hit, good regs will pick up on that in no time.
Keep in mind, there is nothing wrong with raising AK pre, cbetting a good flop (an entirely different topic), and then giving up. You put money in w AK because you are probably the favorite at the time. But, it's still a drawing hand. Sometimes I swear I go an entire night w/o flopping TPTK....well except for the times someone else flops a set!
And, as other people have said, your preflop raise should be bigger. A good rule of thumb is about 1 bet larger than a pot-sized raise when you are OOP.
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