If I wear both light and heavy armor and have perks for both of them do both of their perks activate? Like how I can resist 50% more with heavy armor but regen 50% stamina faster with the light armor.

i need to know, anyone know this?

You should create two saves, one before you spend your perks and one after..

Than you can use the save for after you put in both perks and test it out, than come back here and report. If it doesnt work out, than use your before save.

I would have imagined it activating the perk only when wearing the required type of armour.
ie. '50% less stagger when wearing only Heavy Armor' would not apply if you wore any light armor.
and 'Stamina regenerates 50% faster in all Light Armor: head, chest, hands, feet' wouldn't apply if wearing heavy armor in said slots.
So if wearing a mixed set I would assume neither perk would activate. Always worth checking as someone said

Don't forget mages get higher alteration bonus if they wear no light and no heavy!