Whew! Okay, so after many many hours of research, experimentation, and number-crunching, I'm finally done. I've collected tons of data, and I have a few interesting finds.
1. I was right about Encumbrance Level affecting stamina regeneration. At 25%, 50%, and 100% there are changes in stamina regeneration. However, it depends on the armor. Some armor, like Havel's or Smough's, impedes stamina regeneration at any encumbrance level to some degree. Steel does too, however it encumbers very slightly less than the heavier armor. Some armors don't reduce it at all until you are >50% encumbrance. Finally, most light armors don't affect stamina regeneration at any encumbrance level (except maybe >100%).
2. I was wrong about the Encumbrance itself affecting regen. No amount of changing the weight between 0-25% or 25-50% made a difference.
3. Regen buffs from all sources stack with each other additively, meaning if one increases stamina regen by 25%, and another does it by 25%, then using both will increase regen by 50%.
4. Regen buffs will first stack with each other and combine into one number. Then, when they stack with encumbrance-based regen reduction, they stack multiplicatively. Meaning, that if all your buffs give you +50% regen and your armor gives you -50% regen, in total you'll get a +25% buff to stamina regen.
5. Finally, most heavier armors, but also steel armor (although much much less than say iron armor) reduce stamina regeneration by a very small amount beyond what is reduced by the Encumbrance level alone. This reduction is applied per piece of such armor, regardless of which set it is from. I wasn't able to find the exact formula/pattern for it, but the amounts may very well be arbitrarily set by the developers.
There are some exceptions, but this is mostly the way it seems to work. I'll add some of my findings and their relevant stats to the wiki tomorrow. However, there is a ton of other data I took and put into a readable format. It was mostly for my use, but I feel like I should put it on the wiki. How should I do it, and would anybody really want that?
I welcome anyone to contest my numbers or my conclusions. I wasn't able to get as accurate results as I would like with the tools I have; all I've got to work with is a stamina bar and a timer. So especially if you have better methods than I, feel free to contradict my data.