Answer:
In discussing weight, we are assessing the weight of the rider, not the skateboard itself.
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In a frictionless world, weight has no impact on the speed of a skateboard. In the real world, more weight means more inertia, which means the friction of the wheels have a proportionately less impact on a heavy skateboarder compared to a light skateboarder. Therefore, a heavy skateboarder will coast a further distance on level terrain, or will go faster down a hill, compared to a light skateboarder.