This is a great example of a hand that really doesn't benefit from betting the flop. Mostly it loses the pot when called (because it is crushed by much of Villain's range, and even the floats that QQ is beating will bluff you out), and when Villain folds Hero had the best hand anyway. So, you'd like to check this hand.

The problem is that if you only check hands like this, you give away a lot of information about your holding and give Villain a lot of incentive to barrel a polarized range into your check. Now you have some incentive to check some stronger hands that will be happy to call multiple barrels. Some of these hands, like your weaker Ax, are in the same boat as QQ where they really don't gain that much from betting anyway.

But now Villain has little incentive to bluff, because you are checking only medium-strength and very strong hands. And if the flop goes check-check, you'll have a hard time getting value from your stronger hands on the turn, because you have only strongish hands in your range.

So now you have incentive to check some very weak hands on the flop as well, both to punish opponents who rarely bet when checked to and to punish opponents who fold too much on the turn after checking back flop. And again, because you really shouldn't be able to c-bet all of your air on this flop anyway, those hands don't have anything to lose by checking.

This is how you come to have a pretty wide checking range in this situation.