As far as I know, the only thing light armor has/had over heavy armor was that it weighed less and you could move more freely, but with the heavy armor master perk, it makes you light as a feather as well.

Heavy armor slows you down. My character generally tries to avoid getting hit in the first place so that speed hit is a big no no. I've never had the heavy armor master perk, but I think your character will still get a speed hit for wearing the armor. Someone will correct me if I'm wrong.

No armor : highest speed, most efficient spellcasting.

Light armor : slightly less speed, reducted spell-efficitency

Heavy armor : lowest speed, further reduced spell-efficiency

and ofcourse weight...
there are 0 weight clothes, alowing for more loot to carry on you.
light armour has less weight.. but clearly more than 0.
and heavy armour has the most weight...

however there is a "cheat" around that burdening effect, if you use summoned armour.. that has been made permanent.
(summon an armor-piece... let something attack you.... so it get damaged.... repair it... drop it before timer runs out...
wait till timer runs out... pick it up again..
now you have weightless summoned armour (counting as heavy as far as I know)

Hmm, so heavy armor still slows you down even if it'll weigh nothing when you reach level 100? Didn't know that.

Yes it does.. however there is a "trick"" I use...
I walk on the roads in clothes towards my destenation.. and when getting there.. I put on my heavy armor:):)

strange but true.. with that same armor in your backpack (but not equipped) you walk faster;)
so indeed it's not the weight thats slowing you down.

Well you end up going faster when you have more skill in heavy armor, by the time that you reach 100 in heavy armor, you should be able to run at normal speeds instead of being slowed down.

By normal means, Light Armor is only about half as protective as Heavy Armor, but you get a 50% bonus to Armor Rating when wearing only light armor at Master rank, so they balance out in the end. Both will end up not encumbering you when worn and giving more or less the same damage protection.

The only bonus you get of Heavy vs. Light at Master rank is that Heavy Armor will always be much more durable.

Sneaking is the only benefit that Light Armor gains.