Played this hand a few minutes ago and the turn decision gave me a headache... I wasn't sure if it would be a call or not. The hand was played on Zoom and I didn't have a good read on the player. In the end I made the decision to call, although most likely behind, with a lot of equity. I don't play HU often and I'm a bit of a fish in HU (mostly play MTT's), so these spots aren't normal for me... So, the question is, should I have called or folded on the turn shove and what do you think villain could play this way... (I put him on aces, slowplayed sets, flush draws and two pairs.)

No Limit Hold'em $0.25/$0.50
PokerStars
2 players
Formatted by pokercopilot.com: Poker HUD for Mac and Windows

Stacks:
BTN - BTN ($37.90)
BB - Hero ($66.57)

Preflop: ($0.75, 2 players) Hero is BB with K Q
BTN calls $0.25, Hero raises to $2.00, BTN calls $1.50

Flop: 6 Q 7 ($4.00, 2 players)
Hero bets $2.24, BTN calls $2.24

Turn: 4 ($8.48, 2 players)
Hero bets $4.76, BTN raises to $33.66 (all-in), Hero calls $28.90

River: 9 ($75.80, 2 players, 1 all-in)

Total Pot: $75.80
Hero shows K Q (a pair of Queens)
BTN shows J K (high card King)

Hero wins $75.05

If you put him on aces 2pr and FDs then why did you call with top pair. You put him on a range that has you beat at least half the time. To be honest versus an unknown player I fold here about 95% of the time. Yes that makes me exploitable but it has been my experience that most flop shoves are for value and most hu players are much more competent than 5 years ago. Sure there are random cases when you get sat by someone who is drunk but it's rare. Actually as i am writing this im realizing just how rare flop shoves are in non 3b pots now days. That said I actually might call more frequently because I would know that a competent player is never doing this.

I don't totally agree with the range you assign.

The button limp/called. This range is much more suspect and too heavily filled with combinations of straight draws, flush draws, combo draws, and two pair hands likely 64 and 67. I think you are actually ahead more often than not, but that being said we don't feel comfortable about the call whatsoever. Villain turned out to be a moron but that's not the point.

Even if you are behind you have flush equity to catch on the river either way if villain played a set of 66 or 77 very odd.

Personally, check the turn. That's where i did not like your postflop play. Might go a little smaller sizing on the flop as well.

As played definitely a call 100% of the time.

I played around with weights in poker equilab. You have 49% equity vs this:
So, I haven't done a ton of EV calcs, but
(.49) * 46.90 - (.51) * 28.90 = 8.24
There's a saying to go with TP until you have a reason not to. I'd have folded given no history, tho, but I'm weak-tight.
You can play with his range obviously to make it a fold. I did not include aces or the hand he had. It's a strange-- you might say polarized-- line. Difficult decision for sure.

I think that this sizing means that he is likely not a competent player. When you are assigning ranges to a player without knowing their tendencies you generally give them some hands that a sensible player might choose to play this way. In this case though, limp calling pre and then 2xpot shoving turn means that you simply can't know what range he has. He might have a range that is always and only 58s, he might have only bluffs and there is no sensible way to differentiate. So, when I can't range someone and I am facing a shove, I look at how often I have to call to be inexploitable. Roughly speaking he has bet 2x the pot so you have to call about 25% of the time (if his bluffing range is drawing dead against your holding). So the rock bottom amount you can call to stop him being able to do this with ATC is 25% of the time you take this line.

I don't know how wide you bet this turn but top pair with the nfd is pretty high up in my range. You can never be drawing dead and you are ahead of every semibluff. I would prefer calling this off than 67 or AQ without a fd by a long stretch. Its so hard to say if it will be profitable to always call in this spot but I would never seriously consider folding here. You don't have enough sets and straights to let this go imo