Firstly I think this spot is actually a CB. I don't think this is an ideal hand to check back as it has little chance of improving and it doesn't block a lot. But what would be good hands to check back in this spot to balance my range here? I am thinking AA with suited A clubs, also 6 with nut FD and maybe 44. Thanks

...Tumble weed...

In terms of balance this actually is the type of hand you want to check. A bet doesn't really ever get better to fold, it doesn't pick up much value, and its vulnerable to a raise. But its still strong enough to bluff/catch. Vs tough players you can probably c/c one or two streets and maybe occasionally just check/call all the way down on blankish runouts. And yes you would balance this by sometimes checking other big pairs, with or without draws, quads, or whatever. Also you're just check/folding complete air sometimes and check/raising some draws. A tough player will slow down fearing a slowplay often enough that you're QQ gets to showdown cheaply.

At PLO2 in general though, there isn't much need for balance. Your opponent probably isn't bluffing often enough that a bluff/catch is really that great, and if your opponent does bluff, a lot of weaker players won't slow down due to a "betting is the only way I can win" mentality. So the check/call one or two streets play actually becomes pretty bad. Also, there's more value in betting flop since your opponent will be calling both pre and flop with a wider range, and our hand is less vulnerable to a flop raise since loose/passive underbluff. When there's more garbage that you need to protect against, more garbage that calls, and less bluffing, simply betting becomes far better. Weaker players do stuff like just call flop with a draw or TT and then just check it down.

First of all interesting that you are worried about balancing as a PL2 player. In this pool I think you should bet the flop 1/2 pot and not worry about being balanced. If people were solid you should almost never cbet this flop since your MP range shouldn't consist of any of those cards on the board nor strong draws, so you would get x/r by the BB kinda often if you over c-bet this board frequency wise. So dependent on the players I think you should bet or check your full range here but never pot size.

100% need to be concerned with value over balance at this stake.