There is a problem for dyslexic readers by using extremely high contrast, but it has been greatly exagerated and propagated to the poinpoint of myth (see this seminal report, which nevertheless recommends "to provide sufficient contrast between elements of a page" and "use a dark text on a pale background"). There's also a trend of abuses using unduly light grey text on white backgrounds propagated by popular blogs, mainly by designers trying to achieve a pretty effect, but hurting readability.
Numerous academic papers* show that high contrast text can be read faster than low contrast; the W3C web accessiblity guidelines provide a formula for minimum contrast (see AERT). The opinionated website Contrast Rebelion provides a collection of links to academic research articles on text readability, and a rationale for avoiding light grey on white backgrounds.
*I tried to post a couple, but this site's reputation system won't let me post more than two links. Visit the links at ContrastRebelion site as the starting point for the actual research (I'm not afiliated with the site in any way).