Weather isn't data, a measurement of temperature would be data...
http://en.wikipedia.org/wiki/Data
[Not that I am trying to imply that other things aren't data - but I don't think weather itself is data although you can, of course, have weather data!]
Edit: "There were 5 Exabytes of information created between the dawn of civilization through 2003, but that much information is now created every 2 days."
Obviously there would be plenty of questions, ranging from the most basic (a CD released in 1990 contains 'x' MB of data on it... but there's also the sleeve design, printed track listing etc...) to more complex (how do you measure the data of a painting in computer terms?), but I'm sure if someone were to set about trying to work this out, they could think up (albeit debatable) definitions.
* I have no substantiation for this, but it seems about right: a JPEG is a megabyte or 2, while a single movement of a symphony is 10 or 20, and a short movie at reasonably high quality is easily 100 MB.
Worst case: http://articles.cnn.com/2007-10-17/us/monalisa.mystery_1_leo...
150,000 dots per inch, 13 light spectrums, including ultra- violet and infrared at say 10 bit per spectrum * largest painting in the world (12 384 000 square inches) http://www.msnbc.msn.com/id/14309591/ns/world_news-weird_new...
150 000 x 150 000 x 13 x 12 x (12 384 000 bits) = 4.71279266 exabytes