Does link text "more information" have more weight than a normal link?
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Does the anchor text "more information" hold any additional weight than any other anchor text? My suspicion is no, but just wanted to confirm.
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Not unless you want to rank for more information on the search engines. Anchor text is one of the most important ranking factors; if your page is about brilliant bacon, and you want to rank for brilliant bacon, good anchor text would be brilliant bacon - that's if that keyphrase isn't too competitive and it makes sense to the user.
It also depends what you mean by a 'normal link' - if the normal link contains your keyphrase e.g. www.randomwebsite.com/brilliant-bacon - then that will hold more weight for keyword targeting than 'more information'. There should be a good mix of anchor text linking to your pages though, as would naturally build around the web, so there's no harm having 'more information' or 'click here' linking to your page on occasions.
Here's a brief overview: http://www.seomoz.org/learn-seo/anchor-text