Well the basic idea is that once you master a weapon skill line (that is to say, grind it to level 50) you can use one of two togglable skills to substantially enhance the light and heavy attacks you are using. This would be far from just a simple damage increase though. The skill would use a toggle and use up the appropriate resource to the weapon (stamina for sword and shield, 2h, bows, and dual weapons, magicka for staves) at a fairly high rate depending on the individual skills you used. The drains would happen per use of the skill, regardless of how it is activated.
Here's some of the general ideas of what I had in mind:

One Handed and Shield skills:
Stalwart Posture-
Togglable
While Holding one handed weapon and shield
Blocking while this stance is active reduces the stamina cost of blocking 30%. Light attacks in this posture increase block mitigation by 2% each hit up to 10% maximum. Heavy attacks made in this stance will snare opponents 40%. Shield bashes have a chance to knockdown opponents. After successfully blocking an attack, the next melee attack gains 30% extra damage. All melee attacks drain extra stamina in this stance.
Morphs:
Riposte- After Successfully blocking, the next melee attack gains a 100% speed boost.
Iron Wall- Light and heavy attacks now increase armor and spell resistance 2% each hit up to 10%.

Vanguard-
Togglable
While holding one handed weapon and shield
Melee light and heavy attacks increase the damage of the next shield bash 5% for each hit up to 30%. Shield bashes increase armor and spell resistance for 2 seconds. Successfully blocking in this stance increases movement speed 20% for 6 seconds.
Morphs-
Shield Pummel- Shield bashes now disorient opponents for 1 second and have a chance to knock down enemies.
Resilient Bulwark- Shield Bashes now heal for 60% of the damage they inflict.

Two handed Weapons skills:

Rage-
Togglable
While holding a two handed weapon
Light and heavy attacks gain an increase based on the amount of health the wielder has lost. Damage can be increased up to 200%.
Morphs-
Adrenaline Rush- Movement speed is now increased based on health lost for 6 seconds.
Beserker Rage- Light and heavy attacks now generate a damage shield for 100% of the damage inflicted.

Sunder Armor-
Togglable
While holding a two handed weapon
Light and heavy attacks reduce the armor of the enemy they hit.
Morphs-
Ravage armor- Armor reduction increased.
Expose vulnerability- Light and heavy attacks reduce spell resistance.

Dual weapon skills:

Twin Heavens-
Togglable
While holding two weapons
Attack speed is reduced 30%. Adds 20% dodge chance to weapon attacks. Weapon damage is increased 20% after a successful dodge. Light attacks increase speed of next attack by 20%. Heavy attacks reduce block mitigation by 20%.
Morphs-
Kensei- Successful dodges now inflict weapon damage.
Mushin- Successful dodges restore stamina.

Bloodletting-
Togglable
While holding two weapons
Light attacks now inflict bleed damage. Heavy attacks inflict aoe damage.
Morphs-
Onslaught- Bleed damage is increased.
Carnage- Heavy attack AoE damage now inflicts minor bleed damage.

Bow skills:

Barrage-
Togglable
While holding a bow
Light attacks with a bow fire two shots at 60% of normal damage. Heavy attacks fire four shots at 40% damage. The shots will hit up to four different targets if the targets are in range.
Morphs-
Salvo- Light attacks fire three arrows and heavy fire six. Up to six targets can be hit at once.
Fussilade- Light and heavy attacks snare opponents for 3 seconds.

Rapid shots-
Togglable
While holding a bow.
Weapon damage is reduced 40%. Attack speed is increased 40%.
Morphs-
Arrow shower- Attack speed is increased by 60%.
Hail of arrows- Weapon damage is reduced by 30%.

Restoration Staff skills:

Mending Stream-
Togglable
While Holding a Restoration staff
Weapon damage is reduced to 0%. The healing staff will now directly heal friendly targets for 50% of weapon damage. The staff no longer directly heals the user.
Invigorating Stream- Healing staff also restores stamina in this state.
Communal mending- The healing staff will now restore the health of up to 3 targets.

Vampiric Torrent-
Togglable
While holding a restoration staff
Weapon damage is reduced by 20%. The staff skills no longer heal the user. Weapon attacks only heal the staff user at 100% of damage.
Morphs-
Hemorrhaging Torrent- Staff attacks now inflict bleed damage.
Virulent Torrent- Staff attacks now inflict disease damage over time.

Destruction Staff Skills:


Magicka Swell-
Togglable
While Holding a destruction staff
Heavy attacks fire a stream of the staff element that deals very high damage over time to a single target. This attack is extremely magicka intensive.
Morphs-
Eldritch wail- Heavy attacks also reduce the target's resistance to the element being used. (Note: this does not stack or apply to Eldritch wail.)
Magicka Surge- Heavy attacks add a buildup of magicka that explodes on conclusion of the stream for 50% extra damage.

Maelstrom-
Togglable
While holding a destruction staff
The caster creates a close aoe burst around themselves that remains as long as the skill is active. Enemies take damage of the element of the staff and have a chance to receive debuffs based on the staff. This skill constantly drains magicka while active.
Morphs-
Chaos Swirl- Range of effect is increased.
Elemental Maelstrom- Elemental resistance to the staff element is increased while the skill is active.

These are all just very rough ideas for enhancing weapon attacks. I don't expect any of them will ever make it to development. The ideas are worth tossing around though.