Came across this play last night. Hopefully my format is readable.

SB: --,--
BB: --,--
MP1: --,--
Hero: A,K
MP3: --,--
MP4: --,--
MP5: --,--
Button: --,--

SB: post .01
BB: post .02
MP1: fold
Hero: bet .06
MP3: call .06
MP4: fold
MP5: call .06
Button: call .06
>SB: fold
>BB: fold
POT - .27

RIVER: 9 K 3
Hero: bet .15
MP3: call .15
MP5: fold
Button: call .15
POT - .72

FLOP: 6
Hero: bet .60
MP3: fold
Button: raise 1.20
>Hero: call .60
POT - 3.12

RIVER: 6
Hero: ??

Finish in white text:
Hero: checks
Button: checks

Hero wins with Two Pair (Kings and Sixes)
Button: mucks


So this guy was obviously bluffing or playing a weaker pair, but the raise on the first 6 followed by the second six made me stop and think. Later I thought I should have bet at the river about 1/2 of the pot to seal the deal, and fold if he reraised. Which is the better play?