First Time posting so please excuse the format….

few notes on the table massive chip leader around 160k to my left playing super LAG  but def a component reg no direct history with the villain but he had been running over the table (showed cold four bet shove with A7 off after opponents folded pre) This is a 10 handed table FYI

Blinds are 600-1200 with a 200 ante 

hero on the button 55k AJo

villian(chip leader)  BB 160+

pre flop: action folds to hero makes it 2500, with the intent to four bet a BB 3bet (villain had been 3betting aggressively from all positions). SB folds and BB calls… At this point I'm putting on some pairs 22-66 and some weak connected hands 

Flop: (7600) KK8r villian checks hero checks

Turn:8 (7600) BB leads for 5500 hero calls 5500

River: 9 (18600) BB leads for 20000 hero calls 20000

Final Board: KK889

i think the flop and turn plays are somewhat standard, I could bet the flop but i like to check in these spots and call down on safe run outs against aggressive opponents. Id also check back some 8x as well as Kx, KK for balance. The river is interesting b/c i rarely get there with better than A high i have some Kings in my range as well as 88 and 99 but, i don't think there is much difference between A high and TT-QQ in this spot because I don't expect BB to overbet 9x, also i didn't expect him to have that many Kx in his range as id expect him to 3bet them pre. Basically i beat all his  counterfeit pairs and his random J7o that he plays this way. He does have 8x as well but like i said at the time i thought A high was good enough  to call(plus its almost the top of my range), is it better to fold Ax and call with all my 8x to this sizing? haven't run any math yet i'd appreciate as much feedback as possible ill give results after some discussion, thanks