Russell Seitz says that cyberspace weighs roughly 2 ounces:

A statistically rough (one sigma) estimate might be 75-100 million servers @ ~350-550 watts each. Call it Forty Billion Watts or ~40 GW. Since silicon logic runs at three volts or so, and an Ampere is some ten to the eighteenth electrons a second, a straight forward calculation reveals that if the average chip runs at a Gigaherz, some 50 grams of electrons in motion make up the Internet. So as of today, cyberspace weighs less than two ounces.