I tested the perk and it seems it doesn’t lower the stamina usage on swings.
I did the numbers as well:
State 1 NO PERK - Iron Axe ; 35% Weight
Light Attacks Stamina Usage : 1st 5st, 2nd 5st, 3rd 6st, 4th 7st
Heavy Attacks Stamina Usage : 1st 7st. 2nd 10st; 3rd 12st; 4th 15st
State 2 WITH PERK - Iron Axe ; 35 % Weight
Exactly the same numbers…
I did tests with 98% weight on both, and the numbers are higher, but still same in both Perk / No Perk states.