Hey,

So with the heavy armor perk that makes it weigh nothing and lets you move freely why would I take light armor? seems that heavy armor does the exact same thing but protects me more

I would have to check again to be sure, but I think there is a light armor perk in the archery tree. I could be wrong though.

Ok, just checked the wiki and I had it backwards, the light armor tree has this perk: Wind Walker - Light Armor 60, Unhindered - Stamina regenerates 50% faster in all Light Armor: head, chest, hands, feet
Also you get the weightless perk at skill level 50 for light armor compared to level 70 for the heavy armor, forcing you to take melee based perks to get to the top of the heavy armor tree.