Light and heavy are IMHO decent distinctions. In reality you were wearing plate, mail, scale, or segmented or you were wearing leather, padded, or nothing at all. Heavy and light were true distinctions. I don't think that "medium" ever existed.
When you compare Plate to Chain (And i'm not talking full head-to-toe Prythian chain, that crap was like walking around with 300lbs of iron on your head) plate offered much more in the way of protection, and was, pound for pound, heavier. That said, because of the fact that is was largely self-supporting, it gave more freedom of movement than chain. In terms of literal weight, then, i do agree with you.
However, in terms to relative protection, there is a definate middle ground.
Leather, padded, studded and light-weight-material armours (IE Glass) are light and offer little in the way of protection. They are more for the purpose of redirecting glancing blows than stopping a blow cold.
Chain, reinfroced Leather, and to a lesser extent some banded armours can range, weight wise, from being brutally heavy (Theres a reason Knights were mounted) to relatively light, and offer sufficient protection to turn an average blow of their own accord.
Heavy armours, including most Banded metal and Plate armours were, pound for pound, the heaviest, but actually offered on average more mobility than medium armours. They were also expencive as sin. The Banded iron used by the Roman legions was, on average, worth a small village. There was a particular psycological effect of seeing 20,000 troops all wearing better gear than your king could afford...
On this scale, the actual Light-Medium-Heavy grade is more about protection than weight.
Particularly when you look at the fantasy setting of TES, the middle ground becomes even more pronounced than it would be historically. Where does Bonemould fit? Its not that heavy, but offers sound protection. And Orcish, again a lightweight and comparitivly protective form of armour. Or Troll-bone? Heavy as hell, but not particularly protective at all.
The problem, of course, is that at 100 skill, theres (to my knowlege) no differance between the AC of equal grade Light or Heavy armour. Light Armour SHOULD offer considerably less protection, in return for greater mobility and decreased stamina loss.
The streamlining and lack of impact between Armour choice is, IMO, what dooms the posibility of medium armour, something which should by all rights exist in a fantasy game full of strange materials. Even worse, they go and put in a Perk and a Standing Stone which completely removes any differance between them (The decreased mobility) and renders it as a purely asthetic choice.