So... I think you are looking at poker a bit myopically.
You're asking "how do I play AK", and the question should be "how do I adjust my play for AK"? Right?
First - recognize that AK is never behind even a tight player's opening range. The hand combos of a tight player are primarily AT+, KQ, KJs, QJs and pocket pairs. So you're dominating ALL of a tight opener's non-paired holdings, except QJ. You're not far behind all of your opponent's paired range, except AA and KK, of which you are blocking combos.
So, default by assuming you are ahead. It's never really a mistake to raise when you are ahead. The only mistake is if you are missing value. And this is where you can decide to raise or call. But understand you are making your move FOR VALUE. You actually want to keep hands like K6 in the pot, because you can pick up the hand c-betting most flops, and get very good implied odds
when the King connects. The times that your opponent hits 2 pair while dominated are very slim and you have to recognize this is extremely unlikely. Because if your opponent has K6, he also can have K5, K7, K8, K9, KT, KJ, KQ, probably any suited K. Only two of those hands beat you, everything else pays you off.
When the flop comes K Q 6 RAINBOW (that's very important):
We now re-asses our ranges, and this is subject. Everyone plays the flop differently, and you have to make your best guesses about how your opponent plays hands that are likely behind, hands that are maybe behind, hands that have fair showdown value, hands that are likely ahead, hands that are almost always ahead.
So, this is actually a great board for AK. Because the majority of his range has showdown value AND is behind you. AQ, KJ, QJ all have value. AJ and AT has an over and a gut shot to the straight. The only hands in a tight players value range to smash this are the unlikely AA, and the very unlikely QQ and KK; and possibly KQ. SO - if your opponent has a value hand, it's more likely you are against one that is behind and somewhat unlikely to improve.
Better still: IF your opponent can have K6 here, that puts EVERY OTHER KING in his range, which means you are CRUSHING your opponent's value range.
NOW - the villain leads out. So we are happy, because our hand is ahead of his range. Things get fishy when you raise in position. You have to ask yourself - what will my opponent call, out of position, that I beat? If you don't raise very often, that's going to suck a lot of bluffs out of your range - so your opponent is LESS likely to hold onto KT, or AQ, right? Also - there's no flush possibilities out on the board which removes a chunk of your semi-bluffs. Rainbow flop.
So when you raise, unless you are against a player who is likely to hold onto top or middle pair by putting you on something like TJ, you are going to fold out worse hands, and get called or raised by better. So I think YOUR FIRST LEAK is making a polarizing raise without weighing it against your opponent's tendencies.
Now, since you DID raise - your opponent re-raises you. It's very unlikely that top pair top kicker is going to be good here. You should assume you are behind and looking to improve. I think many players won't even re-raise 2pair here, that's a fairly loose 3-ball OOP.... maybe KQ that puts you on the same hand and is looking to fold a chop.. but I'd say 2pair is the low end of his range. On these stakes, I think TJ is very unlikely, because very few players ever raise-fold on the flop. So I'd say you are pretty much ONLY against 66, QQ, KQ in this spot... and K6/Q6 is only that rare wtf hand. But it's kind of irrelevant. Because the hands that you beat are basically out of most player's range at this point.
LEAK #2 - you shoved. You are never ever ever getting called by worse here. And you are probably never folding out better. Only in the weirdly rare case that your opponent had K6 is a fold even possible... and notice that he tanked called. Your opponent is simply weighing the possibility that you are overplaying your hand against the the odds that you have KQ (most likely) or slow played QQ pre-flop (unlikely). Your opponent is thinking... the only value hand that makes sense for your line is KQ, and I'm blocking a lot of those combos. Maybe you are overplaying AK?
Shoving this spot requires knowing a ton of information about your opponent before even considering it.
All that to say... your leak is that you overplayed your hand post flop, not that you underplayed your hand pre-flop.