I always use the Scavenger, which makes looting quick and the speed I have with these perks is so unbelievable.
So with the Lightweight perk, you get a 15% sprint speed boost if you have only epic equipment. You get another 8% with Fast Exit if you have low ammo in your gun's magazine AND I carry the VMP which is very light and adds an additional 6% with the grip attachment.
With this combination, I have the same speed as the train on the Serpent Island when I'm sprinting, I am not kidding.