E-readers actually get heavier each time a new e-book is downloaded

However, it is extremely unlikely that you will notice. 

Each new text only weighs the equivalent of a single molecule of DNA, which in case you didn’t know isn’t very much at all. 
Prof John Kubiatowicz a computer scientist at the University of California, Berkeley, told the New York Times that each time a new tome is saved, electrons need to be held, fixed, in the memory. 
Although the electrons are already present, keeping them stationary takes up additional energy, which, if my calculations are correct, is, give or take, a billionth of a microjoule per bit of data.
Prof Kubiatowicz, using Enstiens famous  E=mc² formula, worked out that the weight difference between an empty and a full 4GB Kindle would be 0.000000000000000001g.
If I’m honest, I would more than happily carry 3,500 e-books around at the expense of that billionth of a billionth of a gram, than attempt to drag that number of actual books around. Because, off the top of my head, I’d estimate 3,500 books would weigh somewhere in the region of two tons. 
In case you aren’t already convinced, another claim, which doesn’t feel anything like clutching at straws, is that e-readers can also become slightly heavier in sunny weather. This is because they would take on more energy from exposure to sunlight.
Finally, an exclusive world’s first claim that I am about to make! E-readers can also become noticeably heavier if you encase them in concrete. Fact.