I play full ring and I'm not particularly well versed with playing short handed, except for when I briefly start tables or join short ones. Without reads, I have a hard time calling that big of an overbet with just TPTK on a paired board. AA, A6, and 33 are the most likely candidates that have you beat and if villain is loose, there are many combinations of 6x that have you beat. Sure, it's possible Kx, 3x, or even something like TT-QQ could show up, but I'd prefer reads before I put the rest of my stack on the line

A big part of forming ranges is playing an opponent often enough to know their tendencies. Without that, I default to a common, average to good player, and most don't make huge over bets with cards you can beat. I'd probably fold.

Some other things to consider. AK is a nice hand, but that's way too big of a 3bet. Against unknown villains, AK is a hand that you don't want to bloat the pot up too big even if you DO hit your hand and especially if you don't.

The flop check is fine, although if you had a read you could take it down, definitely do.

On the turn, betting is generally good here, although, if the pot is that bloated, you might even consider another check. Remember TPTK is generally a hand you do NOT want to commit your stack with UNLESS you have a good read or reason to. Your bet is too large in my opinion. You're likely way ahead or way behind. If you're way ahead, he's likely not going to call a large bet. If you're way behind, he's definitely going to call or re-raise. I'd probably just bet $0.50, which is a little over 25% of the pot and would keep the pot small and extract value when you're ahead.

One last thought: I've heard more than one professional poker player say that IF you don't know how you're going to handle a check raise that you should NOT bet. That doesn't mean you can't bet and fold or bet and call or bet and re-raise, but you should have a plan. It sounds like you didn't have one, so if you find yourself lost again, you should probably just check here.