For one... it doesn't make any sense. It's based on weight, but weight has almost nothing to do with how armour works. And it's noise mechanics are crazy. A suit of tinfoil is going to make more noise, but weigh less, than a similar suit made of wool. Light armour includes Leather, Mail and Plate, where as heavy is just plate, mostly.. with some mail? The overlap is just silly.

Second, armour does one thing, and one thing only. It mitigates damage when you're hit. It doesn't govern mobility, it doesn't govern stealth, it doesn't govern your ability to look sixy before your morning shower and coffee. It does IMPACT these things, but it's not the driving force, and all forms of armour have basically the same influence.

Third, it creates a poor system for different approaches. Look at the typical dynamic, say, from Morrowind. Mage? You want Unarmoured. Thief? Go Light Armour. Warrior? Take Heavy. All 3 systems do the same thing, and just drive up your AC to decrease damage potential. ALL require you to basically stand there and get hit, and only offer minor differences in an attempt to create any diversity. This is a problem because, A; unarmoured is just a stupid concept - You dodge, your shirt doesn't suddenly become more durable- and B; it creates multiple skills that do the same thing. This means that you end up with homogenised approaches to defense. Everyone looks at defensive options the same way. Level your armour skills, decrease damage.

Fourth, related to the Third, having a homogenised defensive system in turn homogenises damage. Because you need to maintain competitive equilibrium between the 'approaches' you need to minimise the variability in damage as to not overburden any particular 'approach'. You can't have Medium armour behave radically different, or protect against different things, than Heavy or Light, simply because doing so would make each more situational, thus encouraging everyone to use all of them anyway.

First, by merging it into one skill, you can more coherently lump armour together in groups. No longer are things divided by weight, but you can divide them by the technique behind their construction. For instance, Iron, Glass and Daedric are all plate armours, and their behaviour is consistent between them. This allows greater emphasis to be placed on the actual materials used in construction, offering a huge range of crafting options.

Second, because you can link things by construction, you can more coherently define their strengths and weaknesses. Different types of armour have different characteristics. This opens up a few advantages in and of it's self. The biggest one is in damage options. Because you're highlighting the individual characteristics of types of armour, instead of arbitrary weight-classes, you can expand damage types without risk of negatively impacting any particular approach. In particular, you can easily implement Pierce, Cut and Blunt damage types (which runs conveniently parallel to 3 Magic damage types -Fire, Ice and Lightning-) In reality, there's no reason NOT to wear plate, provided you can afford it, but we're not talking about Reality here. The real world doesn't have to deal with Magic. The easiest way to deal with it is to make is so the more metal, the better the physical resistance, but the worse the magical resistance. That idea can be diversified somewhat to make individual armour types more specified, but anyway...

Third, as an offshoot of 2, means that you can diversify weapon types by doing this. Suddenly the differences between Rapiers and Scimitars, Maces and War-Picks, Spears and Halberds, can be represented, allowing each to have different uses and strengths. Combat suddenly becomes more thoughtful and strategic, rather than just being a sloppy slug-fest.

Fourth, it focuses defensive approaches and helps add diversity to gameplay as a whole. If we look at the 3 primary paradigms of the game, the Warrior, the Thief, and the Mage, then Armour becomes the Warrior defensive approach. It's about minimising incoming damage. a PURE Warrior approach would rely almost entirely on reducing incoming damage through things like Blocking, Parrying and Armour, and dealing with problems head-on. The Thief, then, becomes more focused on total avoidance. Between dodging, stealth and diplomacy -It's not about minimising the damage you take, it's about avoiding it entirely-. Mages bridge the two, able to do both, but are limited by their magical resources.

Fifth, by focusing what armour does, you allow other skills to better represent their domains. Stealth isn't determined by your armour skill, but rather your Sneak Skill. Your mobility (including dodging, which should be a thing, even if rolling is silly) is determined by your Athletics skill. You can still have modifiers, such as your armour affecting noise, and total weight affecting mobility, but these impacts are more naturalistic and relateable, rather than arbitrarily linked to specific item combinations.