400nl, I put myself in a weird situation with AA

Villain is 13/10/4 with 3.5% 3bet percentage. I have a useful note that he missed a clear turn value bet with AK on a Kxxx board. No recent history/warring of note.

Preflop - I am confused. We haven't really battled at all and I am surprised to find that he has a 3betting range at all vs. me in this spot. Perhaps that would mean that he has mostly got value hands here and I should 4bet? idk, opinions welcome...

Turn - I think I may have misplayed this street. I was thinking that I could easily rep 99-JJ by checking back and hopefully induce a bluff shove on some rivers, and that I could still shove the river myself to get the most out of KK.

River - Now I am confused again... This looks a lot like KK to me. Time to value shove?

Thoughts on every street welcome.

$2/$4 No Limit Holdem
PokerStars
9 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG ($251.40)
UTG+1 ($410.80)
Hero ($400)
MP2 ($160.80)
MP3 ($194)
CO ($473.60)
BTN ($320.70)
SB ($707)
BB ($400)

Pre-Flop: ($6, 9 players) Hero is MP1 :as: :ac:
2 folds, Hero raises to $16, 4 folds, SB raises to $60, 1 fold, Hero calls $44

Flop: :7s: :qc: :8h: ($124, 2 players)
SB bets $68, Hero calls $68

Turn: :7d: ($260, 2 players)
SB checks, Hero checks

River: :jd: ($260, 2 players)
SB bets $156,

Villain has almost precisely my stats fwiw

What is his 3-Bet % from the SB though? Most people with these stats (myself included) have a ridiculously tight 3B % from the SB, and I think my default preflop with AA would just be to 4B small.

Flop is good

Once he checks back turn his range is still pretty strong so I prob bet small like 1/4 pot or something to set up a riv shove

Once he leads river I'm never raising/folding

Text results appended to pokerstove.txt

13 games 0.005 secs 2,600 games/sec

Board: 7s Qc 8h 7d Jd
Dead:

equity win tie pots won pots tied
Hand 0: 50.000% 46.15% 03.85% 6 0.50 { JJ+ }
Hand 1: 50.000% 46.15% 03.85% 6 0.50 { AcAs }

I guess if he can show up with 77/88 here ever you can think about folding river but you still have ~38% equity and you only need to be good 27% of the time.

I would not be betting KK on the river though in his spot but he might

I have no idea what his 3bet from SB % is. I haven't got enough hands on him for this to be remotely accurate (especially because what I really want is 3bet EP raise from the blinds) and my HUD doesn't show it.

I think I should have just 4bet preflop in this spot, but I just found it really weird because I don't play any hands in this way and I didn't think he would either...

pre is fine and i'd bet like $60 on turn