Buy Light Armor training

From the looks of things the only differences between the two skill trees are,

• Tower of Strength (Heavy) 50% less stagger vs Wind Walker (Light) 50% Stamina regen rate
• Reflect Blows (Heavy) 10% chance reflect dmg vs Deft Movement (Light) 10% chance avoid dmg

I don't know if you reflect 100% of the damage, thus negating it, but I would assume so, otherwise the light armour would be much better in that respect.

Personally I've been stacking Stamina a little to get around this as I use heavy armour, but then again I can tank much more than my follower who is in Elvan armour. Don't forget that you can move quicker and quieter in lighter armour also. I think it's more about your playstyle. Also extra Stamina points increase your carry capacity.

Levelled rewards scale with your character level (i.e., the level you are when you first receive it) rather than scaling with a skill.

The Nightingale Armor does have 3 levelled variants, so if you're a higher level when you receive it, you'll get the stronger version. Once you get it, however, it will not change, even as you grow in level.

Armor in general scales with your Light Armor skill, but this only increases the Armor Rating, never the enchantment (which is where the levelled rewards differ).