# Balancing bluffs and values

Hello guys,
I have been reviewing a hand in a 3way pot I played few times ago in 10NL and I'm kinda stuck on how I should of play.
Here is the hand:

Pre Flop: (pot: €0.15) Hero in HJ has Ac Kh
fold, Hero raises to €0.25, 2 folds, SB calls €0.20, BB calls €0.15

Both SB and BB profiles are unknowns, so I can't really make exacts assumptions about their calling ranges, but according to the 10NL population I think it pretty much should look like that:
SB [TT-66, ATs-A8s, KTs+, QTs+, JTs, AQo-AJo, KJo+]
BB [TT-22, ATs-A2s, KJs-K7s, Q7s+, J7s+, T7s+, 97s+, 86s+, 76s, 65s, AQo-A8o, K8o+, Q8o+, J9o+, T9o]
I don't really think these ranges could be much wider given the fact that I'm opening in HJ.

Flop: (€0.75, 3 players) As Jc Jh
SB checks, BB checks, Hero bets €0.52, 2 folds

So, here is the problem, I am now pretty sure that I should never have bet AK here since I am not accomplishing anything except maybe getting some value from AQ, value I could have get on the two next streets, but then what hand should I have bet, and using which sizing?
The sizing I used here looks correct to me since I want to be betting polar on this board, and the value hands I would of like to bet are pretty obvious since I am the only one possibly holding nuts such as JJ or AA.
So then I enumerated all the value hands I would be betting using this sizing:
[JJ, AA, AJs, AJo, KJs, KJo, QJs, JTs, J9s]
It makes 24 combos I would be happy to barrel on 3 streets. But then I need bluffs to be balancing with, and this is the part where I'm getting lost.
According to the sizing I'm using, I know that on the river I should have 10 or maybe 11 bluffs, since I should have a bit more than 2.5 value hands for 1 bluff in theory, but is it the same on the flop? I remember reading somewhere that with this sizing for example I should have 1 value hand for 2.5 bluffs OTF, 1 value for 1 bluff OTT, and 2.5 value for 1 bluff OTR, but I can't find the article anymore. Is that right? Because then I don't really know how I could manage to get 60 bluffs here (even though I think it wouldn't be such a great idea bluffing this board so much in 10NL).

Also, since my range is way stronger than theirs, would a 1/3pot range Cbet be that wrong? I am not sure how to do to calculate the EV this bet would generate, but then I probably could be going for 3 streets of value with AK or even AQ, and check back OTR with less good Aces.
I could also get in tricky spots when being checked raise with AK, so I really don't know.

I hope all of this is not too confused, please let me know if I'm missing something here.