During my trip through the tutorial dungeon, I noticed my stamina seemed to recover more slowly with the more weight my character carried. Since I plan on specializing in two-handed weapons, it's important for me to understand what factors increase or decrease stamina regeneration so I can prevent myself from running out of stamina at crucial moments in epic battles. What other factors affect the rate at which I recover stamina?
I don't know about the weight thing. I tested it and I didn't notice any difference. I can't guarantee it though, maybe it has something to do with armor worn, perks etc.
What I can tell you is that there are the following ways of recovering stamina, apart from letting stamina restore over time:
This is mostly from http://www.uesp.net/wiki/Skyrim:Restoration.
Also, as a neat bonus: When you sprint, don't let stamina drain completely, since it will take a couple of seconds before it starts recharging again. If you sprint until you have just a little bit of stamina left, the stamina will start recharging immediately.