i dont like this spot to bluff.
First, line of Vilain is, if he got a king, really a good line vs bluffer specialy from a player who would like to go at showdown without a monster hand (i think about KT , K9, for exemple)
You could have a 2pair/set/gutshot who turned in a str8 turn, but im pretty sure you would have raised these hands at flop, maybe preflop 3bet 66, and probably fold K6.
Here, in bvb + with this drawy flop, if i have a king i put you on : missed flushdraw, missed straight draw who turned his pair of 7 in a bluff, backdoor flush, maybe QK, maybe 87s.
i also like to bet more. In 33$ pot, with strong hands and with air, i like to bet about 30$, i will valuebet that 23$ amount with a SD value hands which wouldnt be a monster. (Here, AQ, 86, Kx for exemple)