Depending on who you ask, the internet weights “About two ounces (60 grams), or perhaps 0.2 millionths of an ounce (6
micrograms), depending which method you use to calculate the weight of
the active electrons necessary to sustain the global network.”

Not a whole lot, is it?
Well, it’s not really the weight of the entire internet.  It’s not the weight of all the wires, cables, computers, and servers.  Just the electricity that makes em all go.
Still pretty amazing….

Read more about it here
http://technology.guardian.co.uk/weekly/story/0,,2096636,00.html