Not a scientist, but my first assumption would be that everything on earth, but also earth itself will double in size, knock ourself around our nice orbit around the sun and kill everyone either flashly or coldly.
Ignoring that problem, or applying the effect to the entire universe, probably not much would happen.
Would the size doubling also double the mass? If it's just size/volume of atoms, then the orbital mechanics shouldn't change too much (or at all?)
The moon is about 384,400 km away, and the diameter of the earth is 12,725 km. So, doubling earth's diameter would be 25,450 km , so we're safe from crashing into the moon with our expansion.
The moon would be about 3% closer (if my math is right), but with no change in mass, I don't think the orbital mechanics of it would be affected. We'd probably knock out all of our satellites from LEO to MEO, though.
(I'm probably wrong or at least off on about half of that, so please correct me if I am)