[CyberDildonics]

I think a much better explanation would be to just say that it partitions the values into a lower and higher half. Then it recursively does the same thing to each half.

After that you just have to understand exactly how partitioning works and get the ranges correct.

[NetMageSCW]

How do you decide which weight to use to create two halves?

[CyberDildonics]

You use a value called a pivot, not a weight, and there are many ways and endless variations you can read about, including just choosing a random value from the current range.

[tialaramex]

In their example they choose a random pivot, is that what you're asking about?

There are a number of strategies but random will indeed work and is simple to explain.