I always liked the History Channel show The Universe.

AU is NOT used to measure size. It is used to measure distance. 1 AU = the distance of the Earth from the sun (93 million miles). This is not size. It is a distance. It's the same concept why we use different measuring standards. If measuring the length of you table, you use inches. If measuring how far you throw a football, you use yards. If measuring how far you drive, you use miles. AU is just a measurement standard. It makes taking about large distances easier without the numbers being too large to be hard to use and conceptualize. If I drove from one city to another, which is 320 miles away, what if I gave you that distance in inches? It's a huge number and difficult to deal with. After AU, the standard we use is light years.

This is easy to conceptualize. If the universe started from a singularity and expanded in all directions, at the speed of light 13 billion years in one direction and 13 billion years in the other direction, that is at least 26 billion light years across. But space is expanding faster than the speed of light, not to mention ALL space is expanding everywhere. It's easy to see why the observable universe is 40+ billion light years across.

A better question would be, do we have any idea how large the entire universe is, including what we can't see? We must be able to calculate how much of the universe we can't see.