TPTK in bvb vs nit-reg

villain is 13-7 winning reg over ok sample, 70% fold to c-bet but floaty tendencies and likes to think I'm fos. Folds to barrels quite a bit. Check-shove turn? donk river or check-shove? Or is this just fps and i should be going for 3 streets of fat value?

Full Tilt No-Limit Hold'em, $0.25 BB (8 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

BB ($21.69)
UTG ($14.30)
UTG+1 ($30.43)
MP1 ($18.38)
MP2 ($35.81)
CO ($25)
Button ($35.26)
Hero (SB) ($27.16)

Preflop: Hero is SB with K, A
2 folds, MP1 calls $0.25, 3 folds, Hero bets $1.30, BB calls $1.05, 1 fold

Flop: ($2.85) A, 4, 8 (2 players)
Hero bets $2, BB calls $2

Turn: ($6.85) 4 (2 players)
Hero checks, BB bets $3.50, Hero calls $3.50???

River: ($13.85) 9 (2 players)
hero???

i would reraise turn, even shove. on turn bet i think he protects his A pair from a flush draw.

Villain is a reg but limp/calls that's often a pp. b/b/b is a good line with tptk. your turn c/c is good too since he folds to alot of barrels and rarely has a worse ace with the preflop action. i like a b/f on the river of maybe 7-8. you could get a suspicious call from a fairly wide range. c/shove doesn't sound right, he shouldn't have any AQ or AJ hands.

Edit:
I misread the hand, sorry. Villain didn't limp/call but over-called in the big blind. So check/shove is reasonable, he could have worse aces. But I still like a river b/f since I doubt he b/c's worse but he could check behind with worse that might call a bet. If you were gonna check/shove, you should probably do it on the turn.

You're ahead like a trillion percent of the time... I think whatever line gets the money in sooner is the one you should go with.

I dont mind the turn c/c if he is floating lots then folding to turn barrels. Bet river $9, I doubt a 13/7 calls a shove after your turn check. Hopefuylly a worse A calls

If you're thinking of check/shoving the turn, please explain why a "pure" would not be a better play (esp. if he's seen you do that shit before with air/draws)? Just asking because I wanna try it one day, just to see what it's like...

Donk-shove river? If your image is fos, you may find a call from a pissed off Ax?