Based on your assumption that he has a rather wide 3-bet frequency (and potentially also a somewhat wide 4-bet calling range ip) I would bet on the larger side here. After his pre-flop call ip he can easily have KK/AA that have you beat, as well as the occasional 88. But other than that you should be ahead here most of the time. with a small bet on the flop you are giving him a great price to call with overcards like AK that could outrun you on later streets. I would also argue that a smaller c-bet gives villain a higher frequency to float or 3-bet widely because he has to commit less money. So a bigger c-bet imo tells you more about your opponents range.

Also think that the fold on the turn is a bit nitty. He should really never have 22,44,84,82,42, K8,K2,K4 here. So you are beat by 88, AK, KK AA, you are blocking most KQ and would exclude any other Kx after the pre-flop action. So his value range is quite small and given your read that he is on the agg side he might just be playing around here. Would also consider calling a small-sized river bet (pretty much on all cards especially if another K were to roll off, would likely fold to an A however, as I think that he might play AJ/AT this way.

Usually against non-lag players, cbet 1/3 pot in 3bp/4bp is ok, but vs a lag I agree with Hans, is better a bigger size, maybe 60% pot. Your check ott is beautiful for an aggressive villain, since he can bet at least anything, both value and bluff (and his small size seems a valuebet here).

The thing with 1/3psb CB OTF is it relies on having some fold equity, so you're accomplishing what a larger bet would do but for less money. It is important to do this with hands like TPTK as well as when you miss on non-wet non-middle card flops. However, your hand here is strong but fairly vulnerable. Vs a villain who 3bets wide, and very likely is floating IP with air in order to bet turn after CB otf/ check turn, he could be doing this with a very wide range. And vs hands that won't fold, there are the few that beat you, but there are a lot of other pairs that will call. So I would exploitatively bet larger, as much as 2/3p. As an aside, CB flop/check turn is usually a -EV line, so you want to do your best to avoid having to do that with hands you intend to fold to a bet after checking. Preventively BTW, not once the over card comes.