At first I also thought about raise/folding, but now I'm wondering what his callingrange preflop is.
He only has a gap of 2% between VPIP and PFR so he's generally not calling too much preflop.
So his range should be limited to something like PPs, ATs+, AJo+ and KQs (maybe KQo).
I don't think he'd blufflead, so I exclude 22, 33, 55, 66 and 77 from his range as well as AT, AJ and AK without FD.
Maybe he sometimes does it with some 99-JJ combos, to represent those I put JJ in his range.
So we're up against: JJ+, 88, 44, AQs, KQs, AQo, AsKs, AsJs, AsTs and have 51.3% equity:
Board: 8♦Q♠4♠
Equity Win Tie
MP2 48.62% 47.37% 1.26% { JJ+, 88, 44, AQs, KQs, AQo, AsKs, AsJs, AsTs }
MP3 51.38% 50.12% 1.26% { KK }
If we raise he's going to fold the midpairs like JJ, so we have:
Board: 8♦Q♠4♠
Equity Win Tie
MP2 55.71% 54.22% 1.49% { QQ+, 88, 44, AQs, KQs, AQo, AsKs, AsJs, AsTs }
MP3 44.29% 42.80% 1.49% { KK }
We're a slight underdog vs this range, but I think since he is likely to 3bet 44, 88 and QQ but none of the other hands, we can play pretty well against his range, especially since we're IP.
As played I think you should call the turnbet because most TAGs will be in b/f mode with all Qx, and against his range we're still doing ok (we're an underdog, but we have the equity to call):
Board: 8♦Q♠4♠ 2♠
Equity Win Tie
MP2 56.75% 55.50% 1.24% { QQ+, 88, 44, AQs, KQs, AQo, AsKs, AsJs, AsTs }
MP3 43.25% 42.01% 1.24% { KK }
On the river it's close.
I think he would bet bigger with nutflushes to get max value, so there are sets and TPs left in his range.
Even against a worst case range (without any AQo) we have the equity to call:
Board: 8♦Q♠4♠ 2♠ 4♥
Equity Win Tie
MP2 72.97% 70.27% 2.70% { QQ+, 88, 44, AQs, KQs }
MP3 27.03% 24.32% 2.70% { KK }
So imo it's a call, too.
