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Villain: 814 hands, 19/16, 3bet: 6%, WtSD: 30%, W$SD: 50%, Flop c/r: 10% (not only 3bet pots), Fold to cbet: 67%

Ongame Network $0.10/$0.20 No Limit Hold'em - 6 players - View hand 1842359
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UTG: $12.30
MP: $37.50
CO: $20.00
Hero (BTN): $21.98
SB: $19.80
BB: $36.26

Pre Flop: ($0.30) Hero is BTN with K K
1 fold, MP calls $0.20, CO raises to $0.80, Hero raises to $2.40, SB calls $2.30, 3 folds

Flop: ($6.00) A 6 7 (2 players)
SB checks

Hero?

Bet or check behind? If we check, what is the plan on later streets? Call one or two streets?

I would bet on the flop, villain could have called us here with TT, JJ, QQ, maybe AQ.....His fold to C bet is high enough where in this spot after villain checks to us we should bet.....If we get called I would just check the turn and maybe the river....It's possible if villain has AQ he might just check call on every street.....I feel like here if villain had AK he would have led into us, or possibly 4 bet us pre-flop....

The problem with betting is we are wa/wb and if he calls we are likely behind.
The upside is we know where we are.
The board is really dry so we do not neccessarilly need to bet our good hands.

since the 3bet was against the Co there are for shure some weak hands in our Range. So with a hand like JJ he has decent showdown value. Maybe 1 value bet if its checked through.
You got 800+Hands so you should have some clue what he is doing but with the Information I got I would check call the flop and fold to a turn bet.
If he checks behind I check the turn and reevaluate

what range are you giving the CO after he calls your 3bet?
remember he's a 19/16 reg.

if, like me, you assigning something like: TT+, AQs+, we can easily bet this flop. vrs even that range, we are a 64% favorite on that flop. the more suited A's you add, and the more PP's you remove, the less our equity becomes.

if we cbet, and get raised, we can assume he's either got an Ax or air (if he's a smart reg, one can easily c/r as a bluff here), and we can easily fold (most likely have more Ax's than air). and if we get called, and he checks turn, we can either double barrel to continue to represent strength, or check for pot control and see a river card. i like checking for pot control more than double barreling based on his 3bet calling range + cbet calling range, against a villian like this.

i.e. we can double barrel more in spots like this vrs this guy if we know he will most likely raise the flop with his Ax hands in 3bet pots. but if he's tricky, then i like checking for pot control more.

if we check the flop, we keep his worse hands in his range, but at the same time, we dont actually reduce it either. so, if he checks again, we can bet / fold, or continue to check and see a river.

I think we should cbet at least one street so our hand isn't face up.

thats not really the right reason we should be cbetting.
because if we know villian has Ax here a ton, why in hell would be throw money at this pot?

Okay. I see your point. Way ahead/way behind and all. I just don't want to tip off a good hand reader.