This sound like the premise of a bar trick, but not so.

Why? Because data stored on flash drives has weight. The difference is almost infinitesimally minute, but it is there. The extra weight comes from flash storage storing more data in memory. The transistors in flash memory distinguish between a 1 and a 0 by trapping electrons.

Really love this science. And it was done by this guy, so you know it must be right. This comes from a 2011 New York Times blog post and the example used was a Kindle, but the concept is the same for any memory-based device.