Several ways.
Grip is probably the principle problem. It is almost impossible when large amounts of lead is carried to get the optimum centre of gravity for most conditions, once you get beyond lead that can be carried on the top of the seat, a driver carrying weight will almost always be driving a kart with a lower centre of gravity. It is also much more difficult for a driver to create or lose grip when required, by leaning, because they often sit much lower in the seat.
Next up you have the chassis dynamics, most chassis simply aren't designed to have solid masses of weight bolted to them, they work much better when the weight is dynamic.
Finally you have the ratio between the weight of the driver and the weight of the kart. A heavier driver in a lighter kart has more control and for any given level of effort will get less fatigued.
It greatly exagerates the effect, but imagine a race using powered wheelbarrows where you had to make a certain weight. The lighter person with a fully loaded barrow would find it much harder to control than a bigger person with an empty one.
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