Q: If you were to suddenly transport to Jupiter, what would happen to your mass and weight?
A: Your mass would not change, but your weight would change a lot because of gravity. Jupiter is a big planet and if you decided to go near to it someday, you or your spaceship will be sucked into Jupiter because of it's gravity.
Cells are pretty much the opposite of empty rooms. There are many organelles and processes happening in them, so there's no space for empty rooms. Even when there are spaces, which anyway would be full of liquid, these spaces have a purpose.