I take it you mean the distance, not the size, of what you see?
I'm not sure of the process and math they use to date the universe, but it involves light.
and since the furthest light is coming from 13 billion light years, we also know how far away that object is.
13 billion times distance light travels in a year gives you an astronomically big number.
one of those astronomers or astrophysicists here will have to explain it a lot better, but point is
there is no illusion to the expansion of the galaxy, and it's not due to some magnification force.
All a man's knowledge comes from his experiences