Check Your Perks
One of the best and easiest ways to increase your carry strength in Fallout 4 is to pour skill points into the Strength perk. Every time you add a point into the Strength stat of your SPECIAL perk tree, you’ll gain an extra ten points of carry capacity. If you’ve already maxed out your Strength stat to the full ten, then look no further than the Strong Back perk, unlocked when your Strength has reached six.
The Strong Back perk increases your overall carry weight by 25 for rank one, 50 for rank two, and in its later ranks allows you to use action points to run while overencumbered, and fast travel while overencumbered for its final rank. This final rank of Strong Back means you can head back to a settlement and dump all your junk, without painstakingly walking for three hours to get to your nearest settlement. Finally, if you choose to wander the wasteland alone, the Lone Wanderer perk under the Charisma stat will boost your carry weight by 50 on rank one, and 100 on rank two.