I think "Big Web" is a profile hosted on "cloud infrastructure" owned by a company with public stock. Whereas "small web" is a website you build/create yourself and host on your own server?
But what is "your own server"? Yeah I host my personal site on my raspberry pi, but most people aren't going to do that. They're going to host on a server owned by a company with public stock.
It seems to me like one could market a device that isn't much more than a RPI that would download a container image from small-web-dot-registry that would run a webserver that encapsulates the site one authored on small-web-dot-com.
This image could have some smarts to either punch the right holes through the the router's firewall or do something even more clever with a peer-to-peer mesh network.
At the end of the day, what one would have is a website of their own that they control within their residence. It would foster a lot of this small web spirit and be very cheap to bring to market and maintain.
This tracks with me until I consider the server/client rapport. As far as I can read into the author's intent, this dynamic does not change when someone hosts their own server.
If anything, the "dumb delivery mechanism" only became slightly more trustworthy?