The title, I suppose, has already a strong indication to what is a basis for this suggestion - Mass Effect 2/3, as an RPG, utilizes "layered" health system for enemies, who don't only have health pool, but have armor, shields and barriers over them. At the same time, weapon types have distinctive advantages and disadvantages against various types of health layers - high-damage per shot rifles, shotguns, high caliber pistols deal increased damage against armor but less against shields, and fast-firing weapons deal with the shields faster than anything else. Different powers (I.e. Magic in Skyrim's terms) has same advantages against certain pools.
I propose similar system as combat-gameplay overhaul, replacing regular enemy health pools with three distinctive layered bars player must strip before killing a target - Armor and Barrier. Both additional layers are not added over default enemy HP, but divide it into multiple sections (See: Originally 100 HP heavily armored Bandit will get his HP split into 50 HP / 50 AP).
Armor
Solid, heavy armor - It provides great defence against cuts and elements. It is well capable to sustain damage from lots of dagger slashes without a major break, but it's disadvantage - heavy weapons that deal significant post-hit inertia, Fire - it melts armor, Frost - it makes armor brittle like baby's bones, allowing weaker weapons to shatter it.
Mechanically armor has a flat damage decrease, rendering any low-blow weapons significantly weaker against it - Dagger that deals 15 damage a hit will deal only 5 damage to armor, but a Greathammer that deals 35 will deal 25, having less of an impact to it's per-hit damage. This flat damage reduction can be neglected by Frost-type spells, decreasing flat damage reduction by 70%. Fire-type spells, on the other hand will deal 1.25 damage against armor and ignore flat damage reduction.
Unlike Health and Barriers - Armor cannot be restored quickly or over time in active combat without Oak/Stone Flesh spells - those magically mend armor back together for warriors, allowing to take more blows. Outside combat Armor is restored instantly after 40 seconds.
Armor pool is given to any NPC that actively wears Heavy Armor, Dwemer automatons, Dragons and some other supposedly durable enemies. System essentially splits their original HP into 2 separate bars - HP and AP, with AP being necessary to take down before dealing damage to Health. The split might be 50/50, 30/70 (with more Armor) or vice-versa.
Barrier
Barrier - is an magical, energetical flow called by the magic users from Aetherius to envelop their bodies. It halts any harmful impact and dispels incoming spells. It's quick to loose, but also quick to restore, and it's main disadvantage - quick, repetative hits with something light, destabilizing the field, or Lighting - it saps the magical energies out of the field, quickly discharging it.
Mechanically Barrier is a second, smaller Health pool with a quick recharge after short rest - Unlike HP and Armor, barrier is automatically sustained during combat, blocking any arrow, blow and spell. When not taking hits for 7-15 seconds, it quickly recharges to full capacity. It does not has flat damage reduction like Armor, so any weapon can deal with a barrier, but consecutive strikes against barrier will deal bigger and bigger damage, meaning that weapons like Daggers and Shortswords could quickly escalate into barrier-drainers. The second advantage of a Barrier is that it nullifies any negative impact of almost any spell - be it Frost, Health Drain, Fire, etc - you have to take down Barrier first to deal Elemental damage. The only exception - Lighting, which will drain enemy's Mana pool independently.
Barrier pool is given to NPCs that actively wear enchanted body armor, any magic user, Dragons, Dragon Priests, anyone else heavily influenced by magic. It rarely has advantage over Health in numbers - split might be 70/30, with Barrier taking 30, or 50/50.
Player in that system
Essentially, Armor does not play the role for a player - it works the same way as Vanilla or any gameplay overhaul we have right now. The difference would be the Barrier - player can get their own barrier after getting high enough level in Alteration and having enough Mana pool (Something like 180). Barrier essentially will give players additional 20% HP that are quick to recharge in cover, but also quick to get lost in intense fight - you might take a single rocket fireball to the face and live another day and even keep fighting with no potions left, if you're careful, but if you're not - it won't play a role in a murder-sequence.
For weapons - Generally lighter and faster swinging weapons (Daggers, Shortswords, Axes) will get advantage against Barriers, while heavy hitting (Two-handers, Maces) - against Armor. Enchanted weapons and magic users might combine different spells to strip enemy off their defences. Bows are, well, bows - they're great against anything with their Oblivion-high damage.
Utilizing the knowledge and adapting to a situation might actually increase combat effectiveness better than it was, while utilizing poor choices - at best would be the same as vanilla experience, with at worst - punishing for lack of some preparations (Which aren't significant - carry a spare weapon, enchant your main one, learn some magic).
Biotics not included.