The Weezer wordmark font is not exactly Century Gothic, but rather a slight variation of the true font, Futura Medium. The original logo font appears on the cover art for The Blue Album, Pinkerton, Maladroit, The Lion and the Witch, Make Believe, and The Red Album. Century Gothic has appeared, possibly as a mistake, on various pieces of merchandise and most recently on the first release of the digital album art for the "Pork and Beans" single.
It is also worth noting that a font very close in appearance to Century Gothic is Avant Garde - the name of Rivers Cuomo's first professional band. Coincidence?
Century Gothic is a fairly common font, and usually comes standard with most operating systems and word processing programs. It can also be found for free download all over the net.
Font origin and family
From a Microsoft font website:
A design based on Monotype 20th Century, which was drawn by Sol Hess between 1936 and 1947. Century Gothic maintains the basic design of 20th Century but has an enlarged 'x' height and has been modified to ensure satisfactory output from modern digital systems. The design is influenced by the geometric style sans serif faces which were popular during the 1920's and 30's. Useful for headlines and general display work and for small quantities of text, particularly in advertising.
From a font enthusiast website:
Century Gothic's origin is Monotype's 20th Century, and was a very close clone of Futura. In reproportioning 20th Century to become Century Gothic, the result was a face that is neither Avante Garde, 20th Century or Futura but is something new, surprisingly enough. Of the whole set, this is perhaps the most interesting face for that reason.