If doubling a chocolate mousse, should gelatin be doubled as well?
You need to double the gelatin, as it’s responsible for the texture and “stiffness” of your mousse.

You don’t have to double the water, but you can, of course. The water is no essential ingredient, it’s just a means to dissolve the gelatin. But of course the gelatin will dissolve easier, if enough water is present, so I personally would use perhaps 1.5 times instead of double the water amount. 

Please note that this answer is only valid for the kind of recipes where gelatin is dissolved in a small amount of water and used to thicken a larger amount of cream / mousse / cream cheese or similar. For recipes that dissolve the gelatin directly in the liquid, e.g. a gelatin dessert or jello, this liquid is an essential ingredient and must also be doubled.