This discussion exists on many levels. Here's one.

You may think (and some literature will agree) that there is a theoretical (but not a real) benefit to having a bet size that is appropriate to the strength of your hand. Namely, a bluff should be only big enough to induce the folds you want, but no bigger as you'll lose more money when behind - similarly a value bet should be as big as possible while inducing the calls you want without getting too many folds.

If you establish this pattern anyone will know if you bet small you're bluffing and if you bet big you're betting for value - they'll call your small bets and fold to your big bets.

While it is possible to go opposite what you have gotten other people to expect this is not a safe and reliable thing to do. It requires a lot of ability to read your opponent and it's hard to do online. You often end up leveling yourself rather than your opponent.

A recommended approach for beginners to simplify their decisions is to recommend that they always bet the same amount regardless if they're betting as a bluff or for value. As mentioned in PNL a 2/3 PSB is rarely the best bet size, but also rarely very wrong.

This creates the situation where every bet could just as easily be a continuation bet on a missed flop or a TPTK type of hand.

And this is where I begin. You raised preflop from CO and you were called by the button. Your flop is:
:Kc: :Td:

Your hand is:
1) :Kd: :Kh:
2) :Qh: :Jh:
3) :Jc: :Tc:
4) :Ad: :Qs:
5)
6) :Ac: :Kh:

How much and how often do you bet? 2/3 PSB every time?

A lot of beginners get the basics outlined above and will bet air (4 and 5) and hands with good equity (3 and 6) the same to disguise their hands. But when it comes to 1 and 2 above they will often freeze up, worry about getting paid off on their hands and do "something else".

It doesn't really matter what that "something else" is - what it is is a line they only take when their hand is "too good to waste on folds" and it means they take nut hands out of the betting lines (like just betting 2/3 PSB on the flop) that need the threat of a nut hand to give the air in that betting line fold equity.

Something else:
Overbetting or open shoving may get disbelieving calls so you get more value out of THIS hand - but you suck the value out of cbetting, which to be frank is something you need to be able to do profitably a lot more frequently.
Check-raising is good! The pot gets bigger and it's easier to get the stacks in on later streets. Is this only done with super strong hands and never with TPTK? Very readable.
Betting small like 1/3 pot to get him to raise me is interesting too! Even if he just calls me he'll now think I'm much weaker than I actually am and can get him to call my bet on later streets.

There's nothing really wrong with doing something else with your nut hands - as long as you play them straightforward SOME of the time AND, more importantly, that you sometimes check-raise air - that is, take the special and tricky line with non-nut hands. If you check-raise nut hands you are creating an expectation that a check-raise is a nut hand. You exploit that expectation by check-raising as a bluff. When he learns it can be a bluff you do it with TPTK so when he calls you with a medium pair (bluff catcher) he's still dead.

Those who have recently been playing with the ABCD theorem will see how this relates to the theorem. By having a certain amount of nut hands to an action we are creating fold equity that can be exploited by taking the same action with non-nut hands - this is the origin of the C range, and the amount of hands in the C range needs to be in some degree of balance with the amount of hands in the A range.

ABCD is also a simplified model of the actions you take: A is bet/raise aggressively for value (bet/call/raise/shove), B is hands with value that will pay for a showdown but hopefully not too much (check/call), C are hands with draw potential but too weak to call with - they become semi-bluffs (raise/fold) and D are hands with showdown potential but not so much of it that we want to pay for it - or hands with no potential. Here we check, and if bet into we fold. As someone pointed out in the original ABCD theorem post each of the letters not just designates a hand strength but a betting line / plan for the hand. And this betting line could be check/raise, check/min-raise, bet small/call, bet small/shove etc etc - many more than the ones listed for ABCD theorem. ABCD theorem is simplified and a good tool to BEGIN thinking about hand ranges.

The answer to my question could be that with each of the six hands I check sometimes, bet 1/3 PSB sometimes, bet 2/3 PSB sometimes bet PSB sometimes, check/call sometimes, check/raise sometimes - air will also check/fold sometimes. The actions don't have to be weighed identically for the different types of hands. For KK I may do PSB 1/2 the time and even spread of the others - for AK I may do 2/3 PSB 1/2 the time and even spread of the others. For QJ I may check/raise half the time etc. The weighing doesn't have to be even - you can tweak it towards maximum profitability - but each line you take does need does need to contain a small sample of each hand type. No, obviously don't check/fold the nuts and check/fold air a lot more frequently than check/calling (but do check/call sometimes).

This really gets into range balancing. When talking about the ABCD theorem and using it as a technique I think (and I could be wrong) that we are not talking about balanced ranges - the opposite of balances ranges is polar ranges and I believe (and can be wrong) that it means you act predictably based on hand strength as indicated by the ABCD theorem: Always bet big value and semi-bluff hands - always check/call medium strength hands - always check/fold weak hands. Polar ranges can be very profitable, and are probably more profitable then balanced ranges against very unobservant opponents. It is also much simpler to learn if you consider that ABCD gives you a correct action for your hand based on what range it is in.

This all begins to relate to Shania as well - many things in poker are connected - but the presentation of the example you post is actually sub optimal - you are creating value for 32o by betting it as if it was AA/KK, but you are firmly entrenching 6bb as = AA/KK and to do that you're removing AA/KK from almost all other betting lines, making all other betting lines less profitable because your opponent knows you don't have AA or KK since you didn't raise to 6bb preflop. And the first time you get caught showing down AA or KK after having bet only 4bb you'll have completely undone the effect of establishing 6bb as AA/KK in the first place. Range manipulation comes with a cost and it's easy to do it sub optimally.