That is to say, what is my ruler that is untethered to the surface of the balloon?
Relativity probably doesn’t work this way at all, but if light did actually slow down, would it be perceived by us as light moving at the same speed across a greater distance?
As to the previous question about relative size. If the universe doubled in size, the objects within it such as atoms don’t also double in size. Gravity and the atomic forces don’t change, so eg the size of stable electron orbits or planetary orbits don’t double in size.
It is not the meter that is growing, that's impossible. Instead you must see it as it is, which is that there are more meters continuously appearing in all of space.