I must have missed something obvious but, for the life of me, I don't know what!
After having followed the light armor path, I decided to follow the heavy armor one...
I finally reached 70 in heavy armor and chose the "conditioning" perk according to which the armor weighs nothing...
Well, nothing has changed! I'm still at 470 weigh in my inventory...
Having now acquired this perk, what am I supposed to do so that my heavy armor weigh nothing?!
With my anticipated thanks!