Similarly curious about this. The intuition I extracted:

Let’s say we have 10 requests, where 9 of them take 1 second to complete but one that takes 100 seconds. The average time to complete a request is about 10 seconds, but if you experience the requests in series, at any given time you’re much more likely to sit and wait in one of those 100 second requests.

So if you imagine a long series of requests from this distribution and place yourself randomly in the series, the average time to completion is just a bit less than 50 seconds.

This is what is meant by t-weighted, that events with a large t take a larger place.

I see it is about a long series of requests. Makes sense. Ill start looking at latency at p99.9 and p99.99 more often now!