All weapons increase your spell damage and weapon damage by the amount listed as 'Damage' when you hover over an item. This is why even though staff light and heavy attacks are based on magicka and spell crit you see an increase in weapon damage when you equip it.
Some magicka builds use 2H sword or dual wield swords because of the higher spell damage because as above all weapons give the same amount of spell damage and weapon damage. Also there are passives namely 'Heavy Weapons' and 'Twin Blade and Blunt' which increase the effectiveness of this weapon even for spells. Some people use 1H and shield and that is to use some 1H and shield abilities to increase survivability in PVP.
The tooltip value of a skill is based off both your magicka or stamina build and your spell damage or weapon damage. For most skills, the tooltip value can be calculated with the formula
Tooltip = a*(Magicka+b*Spell Damage)
You can swap magicka and spell damage for stamina and weapon damage. a is just a coefficient and depends on the skill and b is around 10.5
Without addons you'll have perfect immersion and no idea about numbers.

I read some old posts about how magicka used to give people a spell damage point for about every 40 points of magicka. Then, if the posts are correct, it went to about 1:10.5. Meaning for every 10.5 magicka increase your spell damage would go up 1. A couple of nights ago I wanted to test this, as I'm trying to build the best mag sorc dps I can. I removed all my gear and equipped just 1 item that gave 840 magicka I think from an enchant. My spell damage only went up 10-points! So basically for every 84-points in magicka increase I only got 1 point in spell damage increase. I was wondering if this was a recent change and if anyone else is seeing the same results? Where can I find an official description of how magicka affects spell damage both for the current patch and the one coming? (In case it's changing) Thanks in advance for any feedback. If magicka does not give a significant amount of spell damage, then it seems like a better option for dps on a mag sorc would be magicka enchant on all armo with maybe thief or apprentice mundus stone in all divine traits instead of magicka enchants on the big pieces of armor with infused (to give even more max magicka). The DPS would be better getting the max out of the spell damage or spell crit mundus stones rather than trying to add another several hundred to couple thousand max magicka?