ZOOM 25FR AKo in SB

Pre I want to hide my hand strength.

On the flop it looks great, I go for the check raise but interestingly the bb donks out. At this point I put him on 88/T9/AQ/AJ/AT/A9/A8. I beat more than half of that range but co calls and I want to see what the turn brings before it starts getting crazy.

Turn is a blank and BB continues. CO folds and here I decide between a raise and a flat. I try and decide if I'd get 1 pairs to call and I decide that if I raise here he'll probubly fold all of his 1 pair hands.

River basically makes me a winner against all of his percieved range except 88. When he bets out so big I decide i have to just call. With that bet sizing I dont think T9/A9/AT are in his range anymore.

When he shows with a set of jacks I'm a bit surprised. He had a 20% PFR, but I didn't have a good sample to find out a more realistic 3 bet. Anyways I am "satisfied" with this hand but am still a bit confused overall if I could have done something a different way.

There is very few situations I see myself getting away from this with an over caller. Suggestions would be appreciated.

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.1/$0.25 No-Limit Hold'em (8 handed)

Known players:
[tg]BU$11.43:///////;SB (Hero)$72.47:///////;BB$43.75:///////;UTG2$12.18:///////;MP1$41.34:///////;MP2$18.74:///////;MP3$33.44:///////;CO$27.55:///////;[/tg]

Preflop: Hero is SB with A:h, K:d.
4 folds, CO raises to $0.60, BU folds, Hero calls $0.50, BB calls $0.35.

Flop: ($1.8) A:s, 8:c, J:d (3 players)
Hero checks, BB bets $1.18, CO calls $1.18, Hero calls $1.18.

Turn: ($5.34) 3:h (3 players)
Hero checks, BB bets $3.51, CO folds, Hero calls $3.51.

River: ($12.36) K:c (2 players)
Hero checks, BB bets $8.14, Hero calls $8.14.

Final Pot: $28.64.
Results follow:

Hero shows two pairs, aces and kings(A:h K:d).
BB shows three of a kind, jacks(J:h J:c).

BB wins with three of a kind, jacks(J:h J:c).