6 Max Zoom 25c/50c Hero UTG(174BB)(77) Villain BTN (211BB)(??)

Hero Raises 2.5x, Villain Flats on the button and the BB flats.

Pot ($3.08)
Flop: 7hKsKc
BB Checks, I cBet $1.19, Villain Min raises $2.38, BB fold, Hero Calls.
Pot: ($7.84)
Turn:7hKsKc2c
Hero Checks, Villain Bets $5.74, Heor raises to $17.72, Villain Folds.

So i decide to lead the flop as it is 3 ways and im not holding a K, If i had say AK or K7s i would check but having 77 3 ways i think a 1/3 pot cbet will get called alot by 88-QQ even though alot of TT+ would probably 3 bet pre and maybe some A high. Interested on your thoughts on this cbet. When he min raises it seems as though he has a K so i decide to flat thinking he will continue on the turn very often. So i check the turn and he bets around 2/3 pot, i think he can have any K9-KQ and for him to minraise seems kinda 'fishy' so i didnt think he was hardly ever folding a king atleats not on the turn. Hence why i decide to raise quite large going for around 3.5x and he unfortunately folds. Maybe with the backdoor flush comming in he could be bluffing with a hand like 89cc, 9Tcc that we want to give a chance to hit the flush on the river so would just calling on the turn be fair and if a club comes out lead? check 100%?. I find im confident pre mostly on the flop but the further into the hands is where i get less confident. Would really appreciate your thoughts.