Hello everyone, yesterday was playing some 2/3 live (33 BB effective) and ran into this weird spot. I think my problem had to do with my preflop bet sizing, what do you guys think?

Pot : (1.5bb)
UTG limps 1 bb
MP (hero) 33bb effective. raises to 6bb
SB calls(villain)
UTG calls

Pot 17bb (-1bb rake)
Flop is 36Kr

sb checks
utg checks
hero checks

My thinking to check back is that SB flatting range is towards his stronger range and contains some JJ+ KJx+ at the very worst kicker.

Turn 8 pot 17

SB checks
I bet 10 BB
SB jams for 20

I call thinking that ak checks back the turn is an odd line so I don't put him on a king and I begrudgingly call.
I did not think in the moment that his range contains KK and would possibly slow play this hand as such as well as AA which also beats me. (how many combos of hands is this?)

He shows over pocket 8s and I lose to a set.

I think my bet sizing preflop should have been to 7x which I believe would fold out this hand.

What do you guys think about not betting the flop also? Maybe a smaller size not 2/3 pot would fold out pocket 8s as well?

Lately I've been trying at the higher limit at my local casino because of the higher rake at the lower limit.

Thanks for you input,
H