*w/ KK on river 92T7Q what was the river action? I don't see it on weaktight.

*also what do u mean anonymous fast tables, is this ignition?
That would be helpful to know what website this is on, maybe there is more information about how people play and some of the spots would be more sense.

*4bet sizing with KK generally is going to be too large unless you have a clear reason why, other than you have KK lol.
Opening KK to 3bb, and getting 3bet to 11bb sitting oop, 4betting to 36bb here with any hand, doesn't make a whole lot of sense. I believe we are going to make more money by having a smaller 4bet sizing to allow the weaker sections in his range to come along and not hero fold preflop.
Lets say he is 3betting something like this preflop "TT+, AJs+, KTs+, QTs+, AQo+", maybe a little bit tight or loose, I don't know the player, but the 11bb 3bet is quite large so im assuming he is a little bit stronger, if we make it 36bb, honestly his continuting range may only be "JJ+,AKs,AKo", which is a pretty big lose in EV with this hand.
If we 3bet from 11bb to 25bb, with 100bb stacks we are going to allow him to continue with all of weak suited boardway hands that we are dominating, even with his AQs hands that have a lot of equity against KK, they still aren't going to be able to realize all of their equity, we could even make it a slightly larger 4bet, going to maybe 27bb or 28, but 36 is making so many hands that we have dominated KQs,KJs,KTs, QJs,QTs fold. If we do get to a flop against this range JJ-TT,AQo,AQs-AJs,KQs-KTs,QJs-QTs w/ KK we are going to be best on the flop 88% of the time and we have 77% equity against this range. If we just are up against a range of AA-QQ and AK, KK only has 57% equity.

As far as the post flop action I dont see why we just don't bet the flop, anyways x/shoving flop is better than calling we are going to get it in vs a lot of dominated hands that may end up folding on some rivers.
There is $20 in the pot and we have $20 behind, checking Q9x 2tone is not making much sense as 4betting w/ KK especially after we already estabished his range. if we do check, we need to check/shove when we only have 25bb remaining.