NL5 - Facing a tough spot on turn

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NL5 - Facing a tough spot on turn

Blinds: $0.02/$0.05 (6 Players) BN: $5.89 (Hero)
SB: $10.03
BB: $6.01
UTG: $8.32
MP: $5.00
CO: $8.72
Preflop ($0.07) Hero is BN with Q A
3 folds, Hero raises to $0.15, SB folds, BB calls $0.10
The villain is a reg with vpip/prf of 29/23 in 158 hands.
Flop ($0.32) 3 5 Q
BB checks, Hero bets $0.19, BB raises to $0.50, Hero calls $0.31
Turn ($1.32) 3 5 Q 8
BB bets $1.63, Hero calls $1.63
Pot odds are 35,6%. I run diffrent scenarios in Flopzilla in order to see if we should call here. It seems though that if my assumptions are good then calling is very close to 0 EV. Anyway, I want to ask if he would play like this a hand like AQ or KQ on turn. If he doesn't then this is an easy fold.

Here is one of my assumptions for this spot: Always calls AQ pre. Raises 50% of the time AQ on flop and 33% of the time KQ on flop and also sets 100% of the time. Didn't include Q5s, Q3s or 53s in his pre range. Also raises 25% of the time 64s. On turn cbets sets and TP always but doesn't for 64s. It's weird because why choose such a big sizing with that bluff. Our equity vs this range is 33%.

He might be raising though AQ and KQ 100% of the time on flop and if he cbets those here then this is an easy call. I don't know if I should call here. It depends on villain. What do you think?
River ($4.58) 3 5 Q 8 Q
BB bets $1.02, Hero calls $1.02

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