IFold,
Against this type of player I often just over limp 66 because of how often he probably peels the flop light. In this case there are very few gut shots, or any other hands he could reasonable peel that light with. He'll probably call with K high though
Anyway, I bet this flop because your hand is probably best, but is so vulnerable. He has a 22% raise % so he's less likely to have an A or a pp >66. If he calls, I'm shutting down cause the flop is so dry and you have SD value with any pair against a villain like this.
Edit: another factor to consider when deciding to c-bet is the double barrelability of the situation. In a hand like this, double barreling would be very bad, so if I had a hand with less value than 66 I would consider just checking. Probably not on a board as dry as this, but something where he could show up with more gut shots, peel with A high, etc.