This is a drawing of a worn and battered Peter Wright anvil. They are some high quality solid wrought iron body anvils with a steel face welded on.
The issue with anvils made of a solid wrought iron body is that they have a tendency of sagging in the middle where most of the hammer blows are placed down onto the work piece being forged.

Smiths tend to find a "sweet spot" where the rebound on the anvil is best and the work goes on a lot more effeciently.

While hammering in the same area over and over and over, day in and day out, week after week, month after month and years later tends to make it sag. Another reason for that is the fact that the smith may not have cooled the face of the anvil to preserve the temper of the steel that has been welded on.

When looking at old anvils, you may come across a big line between right near the length of the top of the anvil, that is a seam from forge welding on the steel face. It's not a defect, it's just part of welding iron and steel with a hammer and heat.
Some anvil dealers and companies (as well as some small smithy shops) are able to reforge the face of the anvil flat so that it is back into working order.
Now-a-days, we don't quite have that luxury, though I am sure some people have some ideas on how to fix that.

Now, let's get into the math area. The numbers you'd find stamped into the right hand side of the anvil (Where the horn faces to the right when you look at it) represent the anvils weight.

I would highly recommend anyone who is actually interested in anvils to go buy a book about them.
Anvils in America by Richard A. Postman. It is 80 dollars and it has a lot of information in it. My favourite section is about the Fisher-Norris anvils.