Okay -- I was only an art major...
"The best thing to do, then, is not read your Kindle on the train, as the conveyance's velocity will only make it even heavier. And thicker."
...but wouldn't the Lorentz contraction make your Kindle appear THINNER on the train...? (Assuming, of course, that the Kindle is held vertically with the height and width perpendicular to the direction of motion.)
The only way that it would appear THICKER would be if it was held with one of the LONGER axes pointing in the direction of travel, and even then the thickness would only APPEAR greater in proportion to the contraction of the affected axis, it wouldn't actually GET thicker.
That's the way that I remember it, at least.