My character can’t run

• When you level up, if you select stamina, you will increase your carry weight by 5 pounds.
• Also for 3 perk points, you can get the Extra Pockets perk in the Pickpocket tree which increases your carrying capacity by 100. This perk does require 50 skill in Pickpocket.
• The Light Armor and Heavy armor trees have perks that let your armor become weightless.
  • Weightless Heavy Armor costs 4 perks, and needs 70 skill.
  • Weightless Light Armor costs 3 perks, and 50 skill.
• There are pieces of armor with the 'Fortify Carry Weight' enchantment
• There are 6 alchemical ingredients with the 'Fortify Carry Weight' property and potions of the same name.
• Finally, if you can find it, the Steed Stone will also increase how much you can carry.

I played pretty much this character exactly, and I'll tell you my findings:

• Alteration magic is pretty worthless. Yes, with maxed out Ebonyflesh, you could be adding 300 points of armor, but there's really not that much of a disadvantage to using "real" armor versus mage robes. With enchanting, you can put similar effects on your armor to robes, and with blacksmithing you can easily eclipse the benefits of the alteration spells, plus it is permanent. Keeping your magic armor up can be quite irritating, and if a fight lasts for more than a minute you're awfully exposed.
• Illusion magic is still relatively useful, even with maxed out Stealth. Shadow Warrior is good for the occasional buggy sneak attack crit, but if you need to hide for any length of time, Invisibility is where it's at. Potion ingredients for Invisibility potions are somewhat rare, especially in comparison to ingredients for Magicka restoration. Muffle loses some of its usefulness in the mid- to late- game, but it's still quite valuable when you're training Sneak and Illusion.
• Enemies are going to occasionally see you, and there are situations where you just can't hide. Don't plan on the shadows being your only defense. Sure, most of the game can be played this way, but things like the Civil War quests require you to storm a fort guarded by 30 or 40 guys in close proximity. They're going to see you, and they're going to hit you. You want to be able to resist these attacks.

Magic

I'd instead suggest Conjuration and Illusion as your magic trees. Being able to summon a "distraction" Atronach goes a long way. You can stay hidden, throw an atronach out, and then take a few potshots while they're distracted. I didn't really take any perks from Conjuration, though, and on the Illusion tree I did just enough for silent casting. Most of the other perks in these two trees just aren't worth anything.

Stealth

From Sneak, I took it all, although I would regret Shadow Warrior except that it is buggy. Sometimes if you sneak/unsneak rapidly near an enemy, for a second they'll lose track of you, and you can get credit for a sneak attack hit if you time it just right. This can be useful in a melee.

I invested some points in Lockpicking, but there's really not that much challenge in the minigame once you get used to it. I mostly just spent points here to keep the minigame from annoying me overmuch.

Weapons

From Archery and 1-Handed, I'd suggest putting points into the initial "damage increase" perk, and not much else. Most of your damage will come from sneak attacks, but having high damage otherwise can be useful.

Archery is super useful in situations where there's nowhere to hide close enough to melee, or when an enemy is across a gap from you or so forth. Attacking from range also means there's less of a chance they'll find you if you don't kill in one shot.

In the 1-Handed tree, the damage increases do count for daggers (they're considered 1-handed) although I'm not sure they're applied before the sneak attack multiplier. Even if they aren't, it's still worth having the extra damage for those times when you just can't hide.

Armor

Take ranks in Light Armor - Unhindered and Wind Walker are both quite useful. In protracted dragon fights, having stamina for power attacks can be essential. Being able to move quickly in high-resistance armor is also a big boon.

Crafting

Smithing, Alchemy, and Enchanting are the backbone equipment-building skills you'll need to be successful. In Smithing, get all the way around the light armor tree to Dragon Armor, which you can then use to create Dragonscale armors. Meanwhile you can improve all of your armor/weapons as you go along.

From Alchemy, I suggest taking just the "Alchemist" ranks. There are other perks there, but by the time you're at 100 Alchemy, your potions will be so powerful and plentiful that you won't really need them. You can learn the ingredient effects on the internet, or via trial and error. Once you know them, you can create potions that have no negative effects relatively easily.

In Enchanting, I'd suggest taking the middle track all the way to Extra Effect. The rest of the perks aren't that interesting by comparison. Soul Siphon sounds cool, but you'll find that by and large Soul Gems are easy to fill, and the benefit it gives you is relatively minor.