Assume I have some physical system, no matter of it's nature. Suppose also that this system can be descripted as some scalar field. So my physical object is just a function q = f(x, y, z). Imagine that we stretched out the space proportionally along all axes by some factor. You can say that my object has changed. It's bigger now. But actually, if you look closely, it is the same. It works the same way. Every part interacts with each other the same way. It's just resized. But you can't detect it (if you have resized too).
So what stops the universe to have hydrogen atom of 10m radius. If every part (every particle, wave, scalar field, vector field, whatever..) is resized then it should work the same way (may be until we get interation with it). So how does universe preserve distance?

P.S. A lot of commenters point out to the consept of measure. Let me clear one thing.
Suppose we take a line segment of 1 m and a line segment of 2 m. How do they differ? The most popular answer will be that they have different length. But how do they differ **internally**, I mean as **sets of points**. Both of segments are continuous sets of points. We can map one of them to another without loss of any point. So this segments have the same internal structure as sets. They are equivalent. This is what I'm asking for. How does the universe differ segments, that are internally the same.