[Rythm]

I'd need a way better read than those stats (assuming that they're over a reliable sample) to not try to get all the money in here. People play bad in 3-bet pots and even a total nit will have a really hard time getting away from AK, which is also a pretty big part of his range here. It just doesn't seem worth it to let cards that scare him off his AK show up just to get some value from QQ, and hands that beat us are too small a part of his range to worry much about here IMO. I'd bet the flop and then call a shove/shove over a c/r, or shove most turns if he just called.

A 3-bet pot with 100 BB stacks and an overpair is rarely the time to worry about pot control, and I don't think this is an exception. If you really want to check a street, do it on the turn. That way you don't have to worry about potential scarecards as much and you'll get at least 1 street of value from AK before something hits that makes him think he's beat. He's a nit, so I think draws having less equity on the turn is a pretty minor consideration and actually a reason to bet the flop rather than check it. You probably won't get any value from those hands while you have them beat, so you might as well make him fold them before they hit. Also, if he will in fact pay you off with a draw, it's much more likely to happen on the flop when his hand has more equity.

Edit: I think he has TT-QQ and AK here a large majority of the time, with TT possibly being a bit less likely than the other hands. If he has TT he's not putting any more money in the pot unless we let him improve and the same may be true for QQ. That leaves AK and JJ, with AK being twice as likely.