Estimating the size of the Deep Web is a difficult task, given the sheer number of web pages involved, and the hidden nature of those pages. However, BrightPlanet, a "deep web intelligence company" notes this:
"...it is important to tap into the rich resources existing in the Deep Web. The last time an extensive study was completed estimating the size of the Deep Web was in 2001 — a time when the internet consisted of only approximately three million different domains. The 2001 study revealed that at that time the Deep Web was approximately 400-500 times the size of the Surface Web.
Today’s internet is significantly bigger with an estimated 555 million domains, each containing thousands or millions of unique web pages. As the web continues to grow, so too will the Deep Web and the value attained from Deep Web content."
Source: Pederson, Steve. "Understanding the Deep Web in 10 Minutes." BrightPlanet, Mar. 2013. Web. 18 Sept. 2013.