The second one clearly isn't really a "law" in any useful sense, just a back-of-the-envelope calculation: plug in the first "law", and the typical size of web pages, and the constant factor that the first law doesn't state, and a figure of 1s for how fast a page has to load before there's little point making it faster, and out comes the conclusion that it's in ~ 2003 that typical pages load fast enough that you can start making them bigger without crossing the annoyance threshold of 1s.
Of course, that assumes that typical web page sizes stay constant over time, which I bet they didn't between 1998 and 2003. I certainly can't recall any time when typical web pages loaded in under a second for me. It also assumes that latency either doesn't matter or scales the same way as bandwidth, which is also a bit naive.
(The original article was written in 1998.)
Not a very scientific proof for this law, in my opinion.