The most important common point I've seen between the Web 2.0 & Web Squared documents and Weinberger is the notion of liberating the second order of order...
Web Squared makes a big deal of the "sensor net" and how this data is being used to re-order other data - from world maps built using Flickr geotags to the information shadows of commercial media. Weinberger talks about collecting this information not only from passive user input but also active user input - from de.licio.us to the vast, constantly in flux pool of knowledge contained in Wikipedia. O'Reilly covered the value of both deliberately user-contributed data and the passive data in his "What is Web 2.0" article: not only through deliberate sources like Flickr and Wikipedia but also passively in the form of Google's Pagerank.
All three documents have in common a fascination with Wikipedia - not only that it works at all, but in that it actually works quite well.
"Wikipedia, an online encyclopedia based on the unlikely notion that an entry can be added by any web user, and edited by any other, ...is already in the top 100 websites, and many think it will be in the top ten before long. This is a profound change in the dynamics of content creation!" (O'Reilly, "What is Web 2.0?")
"On paper, it sounds like a terrible idea. Build an encyclopedia by letting anyone create or edit an article, even anonymously. Yet four years after its launch at the beginning of 2001, Wikipedia had more people reading its pages than the New York Times' Web site did... its shape, freed from the two dimensions of paper, better represents the wild diversity of human interests and insights." (Weinberger, "Everything is Miscellaneous" pp. 99-100)
At its guts, both the O'Reilly articles and "Everything is Miscellaneous" are concerned with the transformation in the character of human interaction with human information - from the old order of words stored in physical paper with a form of scarcity dictated by the crude laws of Newtonian physics to the new order of data-driven reality, transported in a more Einsteinian and Turing-based world where everyone can have access to a copy of anything that exists if the economic factors are right.