Got myself into a weird spot by not 4 betting I think.

Effective stacks $2k, playing 2/5 hero in the cutoff raises over two limpers to $30 with AhKc, bb (a known pro) 3bets to $130, everyone folds, I decide to take a flop in position since we're so deep.
I should also mention that Villain here is a professional player and sits in the bigger games when they're spread.

Flop: J95 with 2 clubs
pot: $272

Villain bets $120, hero calls.

Turn: 2x
Pot: $512

Villain checks after tanking, hero checks. (Maybe a mistake?)

River: 5x
Pot: $512
Villain overbets to $700, hero ???

I feel like having the Kc is a bad card to hero with here, as the only hands that show up (I think) are JJ and flush draws, as well as AQ, AK.

I think QQ+ probably doesn't slow down on the turn and if it did, it would probably not overbet the river and instead go for reasonable value.

An overbet in this particular spot screams "please fold" rather than "please call" to me, the only hands that really make sense to me are JJ or air. Maybe hands like 99 or TT that are trying to get me to overfold overpairs?

I'm not really sure here, it was a very confusing hand, put my brain in the blender for hours.

Why would 99 be trying to get you to overfold? That's 2nd nuts on this board.

I think you're right in that he either has a smaller pocket pair or complete air, although since he's not a bad player, he's probably doing the same thing with his value hands. So I can see 88,TT,JJ,99 all playing this way, as well as all his overcards (AJs+)

The issue for us here is that our hand only beats AQ and KQ, chop vs AK and lose to AJs. You need to plug in values into an equity calc and see what the values are.

Intuitively, I think this is a pretty standard fold. Maybe a lean fold, but still a fold.

Personally, I don't play games this deep (400bb), so I can't comment on the preflop or whether AKo is a good candidate for a 4-bet IP. I think that's V-dependent. A lot of pros like to 3-bet light, but you need at least some playing history to determine this.

I'd fold the river. The problem is that a portion of his bluffing range beats you and he has to be bluffing a lot to make a call +EV.

Very standard as played up to river, and I think river is a very easy fold. Think about all the hands you can arrive on this river with, and as you outlined in the OP fairly well, AxKc is one of the absolute worst possible ones to hero call with. Also remember that facing an overbet we have to call much less often than facing a "normal" bet (MDF here is only 36%). So we only call here with AxKc if we say this is a live exploit spot where you just hero call ~100% of your range (and trust me I'm all for live exploit spots where we do that!), but unless I misinterpreted the OP, it seems you think your opponent is equal skill or better than you, so it's probably not the time ESPECIALLY since you said what you think about villain, but not what he thinks about you which is super super key information if you want to go for a extremely wide deviation.

Flatting AKo is definitely not "weird" here, but if you meant difficult, then OK lets say you make it $300 and he calls, you have $1700 behind in a $600 4-bet pot, is this not also a difficult spot?

It does suck to put in so much money and lose a big pot, but remember you'll hit TPTK with AK roughly ~50% of the time, so sometimes it happens and it's better to lose $250 in this hand than $950!

I’m confused about a minor point in this spot. You mentioned holding the Kc is a negative here for your hand considering a hero on river. But is it really true? On the river, if V is choosing his bluffs correctly, doesn’t he want to unblock clubs, favoring hands like AQ (no club), AJs (no club), so that he can unblock flush draws in YOUR range? Thinking about it that way, I’d reason that holding a club in our hand is fairly neutral.

I do think his turn check can be indicative of a good player balancing with a hand like AcAx or KcKx that doesn’t fear a flush draw, and cognizant of the fact that top and middle set are squarely in your range. At the same time, those hands can go for max value on the river with an overbet. I’d say he’s representing AcAx/KcKx/JJ for value here and balancing by using his worst Ace highs and King highs (no clubs) as bluffs.

Given that, isn’t holding the Ac or Kc considered a good thing from our perspective considering a hero on river?

I’m not very seasoned in solver logic, so if there are any errors to my thought process, please let me know.

His line is pretty consistent with 5x. Not a remarkable point but surprised it hasn't even been brought up as part of his range.

The deeper you are, the less you want to 4bet AKo (and conversely, the more you want to 4bet AKs). Having the Ac or Kc is going to make up a lot of V's Bet -> check -> bluff river range so having the Kc yourself should skew opponent more towards value. Of course, as CIE pointed out, opponent should also have a good number of bluffable hands without a club and he should be less inclined to bluff with the Ac or Kc for the same reason you should be less inclined to call. In that case, the Kc blocker doesn't actually mean that much.

I think it's a rather trivial fold, and wp prior to the river, but if you have a read that your opponent is overbluffing a lot in these spots you might need to find a call. A lot of people feel that if your opponent is overbluffing you need to bluff catch a little more, but that isn't actually as accurate as it could be. You need to bluff catch A LOT more, basically anything that has his bluffing range beat in polarized spots like this one.

I checked the solver and it does not prefer calling river with AxKc (call: -$30EV). It does sometimes call AcKx (call: $0EV). Idk why. I guess the reason is that AcAx sometimes takes the line of check turn, and overbet on the river, and we block that holding AcKx. Whereas Villain always bets KK on turn (whether holding a club or not). I don't think Villain is supposed to use his club flush draws as bluffs, so unblocking FDs isn't so relevant to the fine points of the hand.
Anyway, this is live poker, and V isn't following solver logic, so he could be turning an underpair into a bluff here, even though he isn't supposed to be doing so. So I'd just fold, since we don't beat some of Vs bluffs.
As Aseah pointed out, when V overbets 1.4x we really don't have to call all that often. We can just defend with Jx and 9x, blocking Vs boats.

Yeah. Theoretically overbetting the pot lets V bluff a lot more for pretty much this exact reason (I think our mdf is like top 40% of our range? AKc is absolutely not in the top 40% of our range based on how the hand played out), but in practice I think we'll all find most of the 2/5 player pool is heavily skewed towards value when they overbet. This makes overfolding to overbets one of the more reliable exploits to a wide range of opponents, and also means you need a really good reason to bluff catch here.

Fold is standard, but you'll come across players where this is a call.

Whiskey Tango Foxtrot???

It's more like 30%.

As a coach, do you recommend Flopzilla to your students? You ought to; it is a wonderful tool for developing one's card sense, and the understanding it brings helps avoid boneheaded blunders like the one above.

It's likely he meant after seeing all 5 cards, not the flop.

^ lol. this, as in the context of this hand. As with any human I'm not immune to being boneheaded at times but this is not one of them. I mean how do you think AK vs. 55 preflop wins ~50% of the time, its definitely not TPTK 30% and making 2pair+ the other 20% :P