3/6 NL AKs facing Aggression

[pokahpaul]

6 handed 3/6 nl on UB

in SB with AKs
one player limps and button raises pot size
i pot him back, limper folds, villain calls

i really haven't been observing villain so i assume he a solid player

flop comes out
K103 with two spades

i bet about 3/4 pot
he calls

turn is a rag spade putting a 3flush on the board
again i bet 3/4 pot
he calls

river is a rag of another suit

at this point I have about 600 and he has a little over 400
i bet 200 as another value bet, folding to a push.
he thinks for a while and comments "hmmm" in the chat
then he finally pushes the rest of his money

i fold

now i was thinking of a probe betting the turn when the flush card came, but then i thought that it would make me look weak and induce a bluff which i probably could not call. i'm not sure if made the correct plays. should i keep firing with TPTK when villain is calling (btw, he spent some time thinking before calling each bet)

my guess is that he probably had aces? maybe AQs? maybe a set?

i later asked him what he had and he says he thought his kings were good and that he thought i was bluffing. perhaps he was lying and was slowplaying a monster hand?

this one hand put me on tilt for the rest of the session so apparently it was a crucial hand for my session.

i'm wondering what you guys think?