The theory:
You can use corner weighing to set up the distribution for each wheel. Essentially you want to set up the balance with 40 - 45% of the weight on the front, 55 to 60 on the rear.
You can use scales, or simply balance the kart on a pivot point (the scaffold bar method).
There's a theory that you can then set the kart up for individual tracks by biasing the weight on each wheel. (If you go round a corner, the speed, grip, and shape of the corner will put different pressures on a kart. What is right for one corner will give less than optimum performance for another.
To make use of such bias you have to be able to drive consistently well, probably to hundredths of a second a lap, rather than tenths.
(There's a film somewhere of F1 practice at Monaco where the filmcrew put a piece of tape on the barrier before the tunnel and Schumacher removed the tape with his rear wheel time and time again.)
As has been said before, all you have to do is sit in the kart on scales and see how much difference moving your head from side to side makes, to realise that either you have to have great muscular control or the best you can do is start from a even balance (which you can do with a pivot bar) to minimise adverse effects.
That said, various people report that the front to rear balance is important, but few people seem to use exactly the same setting hence teh 55-60% range.
What is useful is to set the kart up to a balance and then alter it 1% at a time until you find the best position, then alter it 0.5% from there to test.
Also note that if you weigh 160 kg in the kart, and your wheel base is 1040mm then a 60% distribution puts 1040 * 160 * 60/100 force on the rear wheels = 99840kgmm
and a 55% rear distribution is 1040*160 *55/100=91520, a difference of 8320 kgmm,
And if you weigh 83.2 kg (for convenience) then you have to move your body's C of G 8320/83.20 =100 mm or ten centimetres. (4 inches). Since you cannot move most seats by that amount, you find that many people tilt the seat.
There's also another school of thought that says it is more important to be solid in your seat and in a comfortable driving position than exactly on a weight distribution.
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