KK OOP on an AQ flop

[slickpoppa]

Party 6-max 1-2NL

Villain has 375 and I cover. His stats are 20/11

Villain open raises to 8 on the button and I make it 24 total from the BB with KK and he calls. The flop is AQ8 with two diamonds and I don't have a diamond.

From his stats, Villain seems pretty tight, so if he calls a bet on the flop I can be pretty sure that I am beat. I'm not sure if he would bet after a check with a smaller pair. So is it even worth betting this? Do you think he calls a reraise with 88-JJ enough for betting to be profitable? Against a looser player I would almost always bet about 35 here, but against a tight player I am not so sure.