Weapon choice isnt just about having a dump for the resource you dont use.

Melee weapons (and bows) will restore 10% of your stamina pool when you do a full heavy attack. Destruction and Restoration staves will restore 10% of your magicka pool with a full heavy attack (13% for restoration staves with passive talents).

You really need to focus on one resource or the other in this game. Regardless of how much ZOS tries to stress that 'hybrid' builds are viable, they simply arent as effective. If you want to use magicka, you need to focus on magicka: use a magicka based weapon, wear light armor, gear and enchant for magicka, magicka recovery, spell power, and spell crit. If you want to use stamina, you need to focus on a melee weapon (or bow), medium armor, stamina, stamina recovery, and weapon crit.

If you try to hybridize, you're only going to be reducing your potential. For example, your character is currently using 4 light armor and 3 heavy armor. Each of the armor skill lines has a passive which only applies if you have at least 5 pieces of that armor type equipped. For heavy armor, you get reduced block cost. For light armor, you get increased spell crit. For medium armor, you get increased weapon damage. These bonuses will not apply if you're using a 3/4 mix, so you're already gimping yourself even compared to a character who's using a 2/5 mix.

In general, my advice is that if you want to use spells or magicka based abilities, have a maximum of one stamina ability on your hotbar and gear with at least 5 pieces of light armor and a staff as your weapon type. If you want to use melee or stamina based abilities, have a maximum of one magicka ability on your hotbar and gear with at least 5 pieces of medium armor and a melee weapon or bow.

The odd ability out (that one stamina ability for a magicka build, or that one magicka ability for a stamina build) is there for utility, not damage. Pick something that supports the other abilities you're using. For a spellcaster, you want something like immovable or circle of protection to help make up for your lack of defense in light armor. For a stamina based fighter, you want something that will either heal you, debuff the enemy, or otherwise improve your weapon damage. For a dragonknight this would mean something like spell reflect, molten weapons, obsidian shield, or ash cloud.

Tanks, obviously, are the one hybrid option that does still work better than a pure focused build. Tanks benefit from being able to use both resource pools equally for defense and control, but any tank should still be wearing a minimum of 5 heavy armor.