I agree with Shorty. I mean, where would "medium" start and stop?
Also, it really isn't easy to measure the thickness of a skin. For one, it needs to be shaved first, but many skins aren't shaved. (And I'm not about to go and soak each skin I get, shave it, and let it dry again just so I could measure thickness.)
Second, the thickness of a skin can vary considerably over its surface. I've come across goat skins where the shoulder end was considerably thinner than the tail end, whereas others are more uniform.
And, of course, the skin is thickest on the spine and thinnest on the sides. And, looking at different skins, the thickness increase along the spine is much more pronounced on some skins than on others. Where would I measure?
How well the skin was scraped on the inside also changes things.
Shorty, I admire your determination, using calipers on your cow skins. But is it really worth it? The calipers will reach only near the perimeter (unless you have very costly extra long ones with curved jaws), so the measurement would seem to be not all that useful?
Basically, I just eyeball my skins. If it's looks thin, it's thin. If it looks thick, it's thick. If it doesn't look like either of those, it's medium

I'm afraid, that's about as unscientific as it gets, and I don't see any practical way to change that…
Cheers,
Michi.