If you are an archer, it comes into play later on in the archery tree.
That skill that lets you zoom in with a bow. That skill costs stamina when you use it.
So, the more stamina you have the longer you can zoom. Couple high stamina,
zoom, and the slow down time skill and you pretty much level the playing field against anything.
Other than that and attacks cost stamina, not really sure.
This. First, as a thief you are probably stealing everything not nailed down, so a high carry weight is great.
Second, when using a bow and the Steady Hand perk (especially both levels) high Stamina lets you do near godly things with a bow. You know that scene in the Lord of the Rings movies where Legolas is just rapid fire putting down enemies with his bow? You can do that with high Stamina -> Slow time, aim, fire. Slow time, aim, fire. Slow time, aim, fire.
My finest moment was when I was in a giant room being rushed by undead crawling out of the walls and bursting from the ground. I took out every one of them before they could reach me, putting down a dozen in the blink of an eye without having to move or drink a Stamina potion. THAT is the power of Stamina.