With your read i would check back.The guy is obviously a fun player, so when he checks i think he continues one way or the other and rarely just x/folds.

True you have a good hand to put pressure on his 99-QQ, Ax on multi streets, but just as unwritten rule fun players like to see all 5 after 3betting so hes gonna call you down with his AQcc or w/e and you have to play a guessing game when you brick.He also might lead/blockebet or try to bluff with better just b/c he bricked as well and doesnt know what to do, so it`s really not a great scenario.

B/gii otf sucks as well b/c you have a much bigger edge then to flip 60bb vs a random fun player, so all considered i like the check back.You can continue vs pretty much any sizing ott, and you`ll often get two streets or win a big pot when you hit a flush or a str8 and he randomly starts betting or calling down with Kx that wanted to x/shove otf.