If I start out as a 1/16" inch dot and the nearest 1/16" inch dot is 1 inch away .... as the balloon is blown up and expanded, my 1/16 inch dot expands to 1/8, as does the nearest dat ... and the one inch gap expands also to 1 1/2
(of course none of this is in mathematical correctness, but the principal is the same)
My 1/16" eye perceived the 1" distance and called it 1"
My 1 1/8 eye perceived the 1 1/2 distance .... and called it 1"
Because that's what I had scientifically observed when I was a 1/16 inch dot.
I’m not sure what was Nye talking about in your reference; I’d have to check carefully. If it is about the bodies getting apart, it doesn’t need any special treatment for the observer getting stretched. It is just a bunch of space bodies, all of them getting away from each other. The ‘hard to get’ part, “¿how is it possible that all of them are measuring the rest getting away, should not there be some common point they are getting away from?” is what attempts to be explained by the balloon. There’s no relativity needed here; only bodies that are already in movement and have velocity vectors.
If one wants a general relativity explanation it gets way more complicated. In that case, “gravitational force” would be replaced by “warping of space and time”. The key to understand why the observer is not being warped in a way it would be impossible for him to make any kind of measurement is to notice that gravity is not the same at every point of the universe. A short answer would be “the earth is small, the universe is big, we’re under very little influence, we’re not too warped, we can sort of make good measurements”. The right answer (what I just said is close to a pile of unscientific nonsense - hey, I have, like, a couple hundred words to work with) would require years only to get the very basics right.
All analogies and models fail at some point.