Villain is CB100 with 58 hands. He has Cbet many many times with everyone folding to him

PokerStars - $1.32+$0.18|80/160 Ante 20 NL (6 max) - Holdem - 4 players
Hand converted by PokerTracker 4

Hero (BB): 24.92 BB
CO: 4.99 BB (VPIP: 38.18, PFR: 16.67, 3Bet Preflop: 0.00, Hands: 58)
BTN: 14.34 BB (VPIP: 42.86, PFR: 16.36, 3Bet Preflop: 4.55, Hands: 58)
SB: 11.99 BB (VPIP: 19.30, PFR: 16.07, 3Bet Preflop: 6.25, Hands: 58)

4 players post ante of 0.13 BB, SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 2 BB) Hero has K K

fold, BTN raises to 3 BB, fold, Hero calls 2 BB

Flop: (7 BB, 2 players) 7 2 6
Hero checks, BTN bets 11.22 BB and is all-in, Hero calls 11.22 BB

Turn: (29.44 BB, 2 players) J

River: (29.44 BB, 2 players) A

My thoughts were to check the flop hoping for a dry board and for him to CB then to push.

Im I correct in thinking at low stakes in general you should never slow play however being the large stack here would still leave me with 10BB so I thought it may be correct.

Thanks
Andrew

You can 3beta all in, you can do, what You done...its the same ****, in the long run nothing will change.
Only mistake I could see here is, what if flop was AT7, would You fold or call?