The size of a site bears little or no relevancy to the 'trustworthyness' of a site.

Its trivial to build a 1 page PHP script that delivers a virtually unlimited number of pages.

It's not a perfect indicator, just like the size of a book doesn't tell you everything about its content, but you are still able to make assumptions about the book – e.g. a 1,000 pages book will not be a brochure, and a 2 page brochure can not be a magazine. Sometimes, I land on a Blog, and a simple indicator of its size could tell me how big its archive it. Again, this isn't a perfect solution, it's just one of many criteria you instinctively "measurer": how well a site is designed, how fast it loads, how long the URLs is, what the country domain is, who linked to it, whether or not it uses pop-up – all these sum up for a good first indicator *before* you actually start analyzing the site's content, navigation, author and so on.

No, I don't think this would be of use beyond the most superficial interest. A two-page site might be the most concise source of authorative material on a given subject, whereas a 1,000 page site might be a mass of irrelevant padding.
I wouldn't use this proposed Fx extension.

It would not tell about how authoritative a source is, or how much truth it contains. It is just an indicator of how big the site. Just as you get an indicator of how many images are currently loading, what the URL is, what the PageRank is etc. – one of many subtle indicicators which may be used to judge [your preferred judgment connected to site size]. I would use it, but of course not anyone might.

PS: Here's an example use. You may end up at a single site with PHP code. If the domain is called www.php-tutorials.com and you see "13 pages on this domain" you can pass a good judgment this page is not huge in size, and that you can't find a lot of tutorials. Or when you see a blog, and it has "8 pages" you know either it's new or the author doesn't know about Google – in both cases, you may think "this may be a new blogger." These are all very basic indicators, and they can be used rather subsconsciously (like a site's color scheme etc.)