If everything in the universe doubled in size overnight, would it be noticeable? By my understanding, if everything doubled in size, such as the Sun and the Earth, and because the space in between them (which is nothing) can't expand, would the gravities greatly change and the Earth be pulled into the Sun? 
 A: It doesn't really matter to the atoms if things double in size. It's like the Moon becoming the size of the Earth, it's something 'normal' that happens often in our universe: things become bigger and smaller. Another example is gases of clouds becoming giant stars, that isn't just 'double' but more like increasing $10^{30} $ in 'size' (from separate molecules to forming giant stars)
Note that in some superdense objects (like neutron stars) the strong gravitational force has a direct effect on distances on the molecular scale.
On a side note, remember, not all equations are linear.
Equations such as that for (classical physics) gravity,
$$F_g=GMm/r^2$$
are non-linear. If the distance between two objects double, and their volume doubles while their density remains constant, we have a problem.
(need to add some equations on what happens when doubles)
A: If everything is expanding then that would mean everything. In our point of view the expansion would be imperceptible. As our atoms expand we expand along with everything else including space. This expansion is, in my humble opinion, the reason we cannot accomplish time travel. If everything expands except for our time traveler, who is moving beyond time, within a short time period he would be so much larger or smaller than the rest of the world as to either be larger than the planet or be imperceptible depending upon the direction of his travel. 
A: I had a similar question in mind. If everything double in size we wouldn't be able to perceive that. If we have two identical objects and one expands keeping everything other same then we will know that the object expanded because it was equal to the next one and it is bigger now. But if both of them and rest all expanded by same factor we won't be able to notice it. 
A: If everything expands at the same porpotion it require more enery to do everything beacasue the law of Conservation of Energy states that energy cannot be created or destroyed but be transformed from one form to another. 
