It really just depends on your preferred play-style, or what type of fashion you want to create for your character.
Heavy armor provides better defense, but it weighs more, is nosier when sneaking, and it makes you recover Stamina slower. Light armor is for speedy and agile characters.
There are perks to counter most of the disadvantages that both have, so eventually they balance out pretty equal.
On high levels of smithing and armor schools, both light and heavy reach the maximum damage reduction all the same.
Heavy armors maintain a higher average reduction in the early game, while you can′t improve every kind of equipment to their best tiers and while you can′t get extra armor from the light ones. It′s also faster and easier (as in, using less perks) to reach the highest reduction.
Some people prefer light armors even in the early game on high difficulties because they base their play style on surviving, and thus dodging and not taking damage, more than on killing fast, and thus tanking and taking a lot of damage. This usually applies more to One-Handed builds, but also applies to Bound Weapons, since they don′t weigh anything, and thus don′t slow you down. You can play light armor Barbarian with conjured Battleaxe and be hit very, very rarely while still killing very fast as well.
ps- Light Armor′s mobility is also great with builds that use Block, since you can quickly get the Perk that slows down time at enemy′s power attacks and literally run circles around your opponents.
The thing with shields is also a very valid scenario.
The main thing is - how much will you try to evade physical attacks?
You need to identify all the possibilities you′re against - to put it simply: foes in heavy armor+shield, heavy armor+twohander, heavy armor+sword, Light armor+shield, light armor+twohander and light armor+sword.
Then see where in that you want to fit. If you want to withstand all of them, you go for heavy armor+shield. If you want to evade all of them, you go for light armor+sword. (except clothes, of course)
And yes, the weight of the weapons affects your movement and attack speed, daggers/bound weapons being the fastest, least stamina consuming.
For me it comes down to what suits a particular character build if playing an assassin / thief / ranger type then its light but if its more of a knight in shining armour hero type then its heavy.
Yeah, in the end most things are there to make viable the most different types of gameplay possible.
The most important thing is, that you like the character you're playing!
So, if someone things, that one special kind of armor looks better at him than another, the character should wear it! Just to make it more enjoyable to look at him.