@Breton123
i'll quote from one of the wikis:
Pros and Cons
Advantages (Over Heavy)
Lighter and less movement penalties
Less noisy and easier for sneaking
Perk Unhindered (weightless) is available 20 levels earlier than Conditioning.
Uses less stamina when sprinting
Stamina recovers faster with Wind Walker
Can be faster than the enemy i.e. easier to run from a fight to recover from damage
The lighter weight allows for the carrying of multiple suits of armour, each fine tuned for specific enemies and situations, without drastically taking up encumbrance. Trying the same with heavy armour would leave little to no extra carry weight.
Disadvantages
Much less protective in the early game, however later on with high support skills both armours are able to reach the protection cap.
Bare fist attacks are less powerful without Fists of Steel, though at this time the Fist of Steel perk does not work properly.
Weight and movement penalties from Heavy may be compensated through the Steed Stone, though bear in mind the opportunity cost: a person in Heavy Armor using the Steed Stone wouldn't be equal in the sense that a person using Light Armor would still have a free choice of stone.
Sneak perk Silence muffles Heavy Armor (though it also muffles Light Armor).
Deft Movement only negates melee damage, whereas Reflect Blows reflects it, and the magnitude is the same for both. (NOTE: Mechanics for Reflect Blows is in dispute, see talk page for the discussion).
you may be right about speed but it is available much earlier on (if you power the skill...which i did because i know how important carry weight is in any RPG) also note the point from the wiki about sprint.
another thing to not given all the people saying you can stealth in heavy (and you can...to an extent) is that its not just weight. armor makes noise. light armor make less. even if you enchant both with muffle light armor is still ahead.
tbth tho you can wear pretty much anything you want and still hit the armor cap even if you go for the shirtless Conan look. there are skills and perks that can make that entirely feasible.