Hey guys! I am wondering about this flop spot on bovada. It seems like neither of us really hit pairs on this board so I'd assume the advantage goes to the 4-better who can have higher premiums unless villain is 3-bet flatting 78s?

We have KdJs in the CO, BTN 3-bets us first hand on the table, I go ahead and 4-bet him to 22 bb's pre and he flats.
FLOP: 6c 5h 4h

I c-bet slightly over 1/3 pot and he raises me a little under 3x in position. We fold. Today I looked through my hands and villain showed AdKs with no backdoors. It seems like the small c-bet induced him. What's a better size here? Should we just not c-bet this spot?