I plan on trying this: getting 70 heavy armor to get the conditioning perk, which will allow you to have the armor you wear to weigh nothing, then leveling up my sneak with my weightless heavy armor. Would this work? Did I just break the system?

bump

Why wouldn't it work? It might take a while to level both heavy armour and sneak. you can answer your own question.

Possible, but you need to get hit in order to use heavy armor, which is counter-intuitive to sneaking around.

Also the stealth bonuses and the combat bonuses from light and heavy armor respectively would make each weaker.

Without acrobatics? Or dodge? That's one strange ninja you want there. Not counting the fact "ninja" looked more like farmers than armored fighters.

It's doable but counter intuitive and not using the heavy armor to the best of its ability.