It doesn't work. If you look under active effects in the magic menu, there SHOULD be "Regenerate Stamina" from the perk, but there isn't.
Well, maybe it's working but it doesn't show up there? Nope, if you physically time it, your stamina regen stays the same whether or not you are wearing all light armor or heavy armor.
Just me?

Edit: tested it with FRAPs, to the frame. You do regen stamina faster in all light armor, even though it doesn't show up under active effects.