Someone more proficient than I can describe/explain exactly what corner balancing does for the car's handling, instant center, etc.
But I do know that it can only be done with any real accuracy with an adjustable collar type front coil over, and rear weight jacker/spring height adjuster on the basic suspension type our rides came with from the factory.
Both corner balancing and sway bar preload affect weight transfer between opposite corners.
A car is like a stool with 4 legs. If one leg is short, it will reduce load on both its corner and the opposite corner, leaving more weight on the remaining two. This “cross weight” property is what allows the springs and sway bar to effectively transfer load when cornering both across an axle, but also front to rear (by making one axle stiffer than the other)
For an example that’s more clear to see, when your stiff rear sway bar causes the inside rear to lift in a corner, the weight of the car gets redistributed to both the outside rear and also the inside front. Even in a corner, the four wheels still have to hold 100% of its weight up
Tires don’t actually have a linear friction response (you get less and less available maximum cornering force for each pound you add to one corner as ).
In the case of the rear sway bar, that effect means that the less stiff axle that is more evenly distributed (front) generates more cornering force, and the stiffer, less evenly weighted axle (rear) loses grip, and the result is what we like to call “oversteer”
Back to sway bar preload and corner weights, this means that uneven corner weights means that weight transfer no longer starts from “zero”, and the weight transfer effect will slightly be different between cornering left and cornering right! In this case you’ll find that the car feels different in the two directions.
Taken to the extreme of unevenness, you might find that the car, say, understeers turning right but oversteers turning left, and also generates more grip when turning one way vs the other. This effect (along with unsymmetrical alignment) is actually exploited in oval racing (like NASCAR) to make the car better at turning left than right.
Clear as mud?