Well, they carry the weight by REDUCING their TENSION. So if you've 4 spokes at 100kgf tension and you add 40kg of load, they will each get reduced tension of -10kgf each (assuming all four are loaded evenly). This reduction in tension is caused by the bottom of the rim being flattened and pushed towards the hub by the weight. So now you've got 4x spokes at 90kgf because the distance from the rim to hub as been reduced.

There is debate as to what happens next, whether this missing 40kgf appears at the "hanging" spokes on top or is distributed amongst all of the upper spokes. So far from all the modeling and actual in-the-field measurements I've seen, the 40kgf that's lost from the 4 bottom spokes is distributed amongst most of the upper spokes. The spokes next to the loaded zone actually stay the same and the ones above increase tension. So it may look like this:

4 bottom spokes -40kgf tension (-10kgf each)
2 spokes adjustment to each side of those: zero change
26 spokes above loaded area = +40kgf tension (+1.54 kgf each)

Here's a graph showing the change in stress & strain on a spoke as the wheel turns. At the very bottom, the spoke shows the least amount of load. Notice also that lacing pattern makes minimal differences in the variations of total load.