AKo out of position and my 4bet is called - what calling range am I facing?

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AKo out of position and my 4bet is called - what calling range am I facing?

Blinds: $0.25/$0.50 (6 Players) BN: $30.13
SB: $36.04
BB: $51.79
UTG: $60.74 (Hero)
MP: $50.09
CO: $95.03
Villain is playing 20/11 over 400 hands. 3bet% is 4.6% over 152 opportunities. They;ve only been 3bet 3 teams - all by me (they must be the best game selector). THey've folded once. Their 3bet sizes in position have been 4-4.5x this session. Honestly haven't even seen them make a semibluff but people who raise 11% of the time are invisible 89% of the time.
Preflop ($0.75) Hero is UTG with A K
Hero raises to $1.25, MP raises to $5.50, 4 folds, Hero raises to $12.00, MP calls $6.50
Flop ($24.75) T Q 8
Hero checks, MP bets $8.50, Hero calls $8.50
Turn ($41.75) T Q 8 7
Hero checks, MP bets $29.59 and is all in, Hero folds
Final Pot MP wins $39.66
Rake is $2.09

Preflop, I think a fold is out of the question and I'm left with flatting, 4betting, or if I really reach for it, 4bet jamming. His raise isn't so big that the jam seems natural.

My bet size made sense at the time and now seems way too small so their monster raise.

Questions:
(1) What types of ranges do we give villain?

(2) What calling range do we give this type villain? Will the range be inelastic over reasonable 4 bet sizes? More and more I think so. Thus I think I should've raised a couple more or just flat-called.

(3) Not surprisingly, the solver balances betting and checking the flop with this hand. It also favors a larger bet. I don't think that's necessary against a villain who is unlikely to bluff. However, it also check folds. If I play this as 100% check, should I still fold it?

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