villain is playing 13/11 20%agg over 33 hands.

Poker Stars No-Limit Hold'em, $0.05 BB (9 handed) - Poker Stars Converter Tool from FlopTurnRiver.com

Button ($5.66)
SB ($12.15)
BB ($2.16)
UTG ($5.45)
UTG+1 ($1.68)
MP1 ($2.73)
MP2 ($5.55)
MP3 ($5.96)
Hero (CO) ($5)

Preflop: Hero is CO with 10, A
5 folds, Hero bets $0.12, 2 folds, BB calls $0.07

Flop: ($0.26) 3, 4, A (2 players)
BB checks, Hero bets $0.15, BB calls $0.15

Turn: ($0.56) 10 (2 players)
BB checks, Hero bets $0.30, BB calls $0.30

River: ($1.16) 2 (2 players)
BB checks, Hero bets $0.60, BB raises $1.59 (All-In), Hero calls $0.99

Total pot: $4.34

Are you ever getting away on river? Is it one of those spots where the odds may be good, but it's so obvious that we're beaten?
I don't think that my self, but I'm interested knowing if anyone else do.
Edit: Should river bet be larger? I think AK is gonna call no matter size here, most people would also call with AQ I guess, but it's more on the edge, especially against a large bet. AJ I doubt a villain with these stats would call here, but definately better chance the lower betsize.

you need to bet bigger on flop and turn, which would of made river easy shove.

as played I dont fold river. Getting good odds

I think this is pretty close. You're getting good odds but you beat hardly anything but a bluff...maybe a busted fd i guess. Depending on my image i could go either way but i guess sigh call just cos you only need to be right ~20%

bigger on all post-flop streets, call the check-raise cos pot-odds and worse two pairs

I dont understand going bigger on the flop against a taggy looking guy in Co V Blind situations. I mean he probably never has worse Aces.

Im not expecting to get stacks in that often and i could even check behind here because i think my hand is so strong and he dosnt have hat good a hand that often to continue with.

On flop bet about .20 and on turn .40. I think I check behind on river though. His low aggression % makes the river a fold imo. Would villain 3bet AK from BB? This smells like he has a set to me.

I think checking back the flop turns our hand face up to a villain that can read well and would cbet here 100% of the time. He doesn't call v. often with much worse aces maybe but we have plenty of outs vs better aces and we are obv doing very well against his spade holdings.