“What are you, part pack mule? Though those favoring heavier weapons and armor are likely to take this perk on general principle, it's also hugely beneficial to scavengers; spend more time in the wilderness gathering loot to sell or trade! Carry a greater complement of killing equipment! And at higher levels, have some way of easily maneuvering back to safety without dropping your ill-gotten gains.”— Fallout 4 Vault Dweller's Survival Guide description
With rank 3 of this perk, running while overencumbered consumes AP similarly to sprinting. Because of this, increased Endurance also lowers the AP drain just like it would for sprinting.
Rank 3 of the Moving Target perk also takes effect with the ability granted by rank 3 of this perk, reducing the AP drain of running while overencumbered. It also combines with rank 5 of this perk multiplicatively, further reducing (but not negating) the AP drain.
On Survival Mode, Rank 4 will negate damage taken from being overencumbered.