Each downloaded book does make your Kindle weigh slightly more:

Although the electrons were already present, keeping them still rather than allowing them to float around takes up extra energy -- about a billionth of a microjoule per bit of data.

Using Einstein's E=mc² formula, which states that energy and mass are directly related, Prof Kubiatowicz calculated that filling a 4GB Kindle to its storage limit would increase its weight by a billionth of a billionth of a gram, or 0.000000000000000001g.

This is roughly equivalent to the weight of a small virus, while the equivalent number of books -- about 3,500 -- would weigh approximately two tons.

(Via Marginal Revolution.)