How Heavy Is The Internet?

Using publicly available information, for the first time in the world, we have precisely and scientifically calculated the weight of the Internet. Obviously this information is only really useful to someone attempting to work out the cost of posting the Internet somewhere, perhaps to North Korea. Still, the casual reader may still enjoy learning just how heavy the thing is.

And how much does the Internet weigh?
At least 498,438,559,990 kilos.