Assume a 100bb NL game 6max game. Hero is on the Button on Open raises 3BB with a 55% range 
The BB calls (25% range). On a Board Axx a lot of players cbet a large portion of their range (60% - 90%) while checking behind babyaces (A7-A2) and pocket pairs. But this leads to a very weak c-betting range which can be exploited by check/raising a lot. How could a balanced c-betting and check behind range look like?
The proper balance is going to depend on your opponent's tendencies. Unless both opponents play Game Theory Optimal, there isn't a single correct answer (and even if they both are, we don't know that answer yet!)
If you continuation bet the range that you stated, and your opponent starts check/raising a lot, you can adjust by calling those check/raises with a wider range, including any pair. You would also want to reduce your continuation betting of hands that could draw to a decent hand, but are current useless. For instance, start checking behind stronger broadway hands that could make a best hand with 2nd pair, or pocket pairs that are somewhere between the top and bottom cards on the flop, while leaving some trash like 54s and 65s that didn't connect in your c-betting range. This will nearly polarize your range - if you divided your range into 4 sections, you would cbet the top 40% and bottom 20% of your range. If you get played back at, you can continue with the most of the top of your range, while tossing the trash.
I know what you're supposed to do. You start by tightening your range to about 35% openings. You stop checking back your Ax hands and c-bet call down because that means he's check raising with a polarized range. At the same time, checking back gives away your hand.
So, assuming he will not try to bluff you off of top pair you start checking back a portion of your air range. For example, I will c-bet any Pocket Pair under the middle card; I will bet any suited connectors with back door draws and c-bet ones with out and if he is the kind of guy to stab once, I peel. If he won't stab than I delay c-bet. On 2 tone flops I bet hands with back door flush draw and give up on ones with out and won't call a bet no matter what if he is always betting in that spot, because he knows that I will start to check back my value range and bet everything else.
Hope this helps some of you.
In my opinion, though this is not an easy task, it can be greatly simplified by remembering that balancing ranges usually means choosing between two basic strategies:
Playing different types of hands the same way.
Playing the same type of hand different ways.
An overall strategy which incorporates a combination of both will ensure we do not become too predictable, assuming we are facing somewhat competent opposition.
One way to achieve this is to introduce some randomness into your game. On an Axx board, villain is expecting us to c-bet here almost every time. Let's assign a cbet % of 83% on these types of flops. We then take a dice and roll it and if it lands on ONE, we check behind, but all other times we bet, regardless of our holding. Villain will likely make assumptions about our check-behind range which may or may not cause him to make mistakes. Either way, we can not be exploited very easily.
Two points might be helpful here:
You can strengthen your betting range while achieving another good thing.
If you move some of your weak hands into your checking-back range, then you both strengthen your continuation-betting range and you keep your opponent from reliably reading your hand for one pair when you check back.
It's not such a bad thing to face aggression in this spot.
You have position and there is money left to bet. If he check-raises with a big part of his 25% defending range, he will have a lot of hands you can bluff out sometimes and plenty of hands you will beat sometimes. Since you have position, your situation is not as bad as it might seem given that his raw range is better than yours.
