When it is time to install a sway bar, you first need to chose the correct size, then do a proper installation, and maybe also do a little fine tuning to suit your personal preference and driving style. To this end it will help immensely if you understand how the sway bar works. A prerequisite is to see the autocross video (if you haven't done that yet).

A single sway bar does not change weight of the vehicle, nor front to rear weight bias, nor left to right weight bias. What it does do is to reduce body roll (improving steering response), make tires stand up straighter, and change weight distribution from corner to corner. Making the front sway bar stiffer adds weight to the outside front wheel while reducing weight on the inside front wheel, and vice versa at the rear. For example, in a right turn it could add 100 pounds to left front and right rear while reducing 100 pounds at right front and left rear.

The secret to "adjusting" oversteer/understeer with a sway bar lies in how tires work. The relationship between lateral grip and load is the coefficient of friction. Stickier tires have higher friction and produce higher lateral grip. Lateral grip for a tire increases with weight loading, but is not linear. Increasing load on a tire by 50% may only increase lateral grip by 30%. This represents a reduction of grip efficiency. That is, if you overload one tire by reducing load on the other tire (on the same axle), the total lateral grip is reduced.

The sway bar takes advantage of this principal by transferring weight from corner to corner, thereby increasing total lateral grip at one end while decreasing total lateral grip at the other end. By adjusting stiffness of the sway bar you can adjust the relationship between front and rear lateral grip, thereby adjusting oversteer/understeer. But this only works when all four tires are on the ground, and weight distribution is close to optimal.

When the car is carrying one tire in the air you are on a tricycle, and the sway bar has nothing to do with weight distribution. With half the weight of the car on one rear tire you will have reduced grip efficiency at the rear, and the tail will swing wide in a hard turn (whether you like it or not). If you lift off the throttle at speed the car will likely swap ends (unless you are very adept at driving sideways). It is tough to drive a car in this condition, and not the fastest way around the track.

Additionally a large amount of body roll will tilt the tires so they will tend to roll over a bit onto the sidewall, chewing up the outside shoulder of the tread, and lifting the inside third of the tread width off the pavement. This also reduces grip efficiency by overloading part of the tread while unloading another part of the tread. This affects the front tires (due to kingpin inclination) much more than the rear tires (on solid rear axle). Excess body roll then spoils grip at the front more than at the rear, leading to the characteristic low speed push or understeer with no sway bar, up to a point.

In a fast turn when the rear tire finally lifts off the pavement grip efficiency is reduced dramatically at the rear, and you get a sudden (and maybe unexpected) transition from understeer to oversteer causing the tail end to swing wide. This gives horrible oversteer going sideways in fast turns and doing dramatic (and increasing) tail wagging in slaloms and switchbacks.

Starting with the case of one rear tire in the air, increasing front roll stiffness will reduce body roll, bringing the rear tire closer to the pavement, and improving tire grip all around (especially improving front grip and reducing understeer). Once the rear tire is in contact with the pavement the roll bar can begin to affect weight distribution. Going stiffer up font, reduces weight differential at rear and increases weight differential at front, improving grip at rear while spoiling grip at front. This further reduces the oversteer problem, getting closer to neutral steering that is the holy grail of high speed road racing.

If you go too stiff up front you reduce front grip to the point of inducing high speed understeer. This is not terribly bad for a street car. If you do something stupid at speed the front end will drift to the outside of the turn. If/when you then (instinctively) lift off the throttle, the deceleration will transfer a small amount of weight forward giving better grip up front at the same time as the car slows down, and it will turn in and stay on the road (very civil, nothing dramatic). But this is not the quick way to go racing.

For fastest top speed potential around curves you need close to neutral steering. For quickest turn in for tight corners at autocross you can use a little bit of oversteer. It may also be advantageous to be able to adjust the amount of oversteer depending on track configuration. To do this you need to be able to intentionally induce oversteer, and then you can decrease oversteer as needed (or as desired) by softening up the front sway bar end links. This is where the 7/8" bar is nice for competition (but a bit much for street use).

If you start tinkering with the suspension geometry for serious competition, you might install stiffer front springs and/or softer rear springs, which has much the same effect as a stiffer front sway bar. In that case you can use a smaller sway bar. If you lower the ride height the center of gravity gets closer to the pavement, also reducing left to right weight transfer and body roll, and you might use a little smaller sway bar. If you want to reduce body roll independent of corner-wise weight transfer, then you need to increase roll stiffness at both ends at the same time. This requires stiffer springs at both ends, or increased sway bar at both ends, in which case you also need a small rear sway bar, but only one bar front or rear needs to be adjustable.

If you ever see me crawl under the front end of my MGA with a wrench between autocross runs, I may be adjusting the sway bar end links (aftermarket type). More often I may be tinkering with tire pressure a bit. A softer tire gives larger footprint and better grip, as long as it keeps the tread fairly flat on the pavement. Too little pressure allows a tire to squirm and roll over on the sidewall reducing grip, so there is an optimal tire pressure for best grip. When you have all four tires giving best grip, the way to adjust oversteer is to reduce the grip at one end, commonly by increasing tire pressure a little to spoil grip. Most of the time I cannot get enough grip at the rear for a frisky autocross (too much oversteer), but the run in the video is a rare exception showing too much grip in the rear causing understeer for all turns, fast or tight. This means too much front sway bar, and I need to soften the end links for the street tires.