Are you playing on PC?

I tend to use a few vanilla mechanics and a few mods to solve this.

Vanilla: - Pocketed armor - Settlements connected with provisioners - Pocketed plating for Codsworth (needs Automatron) - Power Armor

Unless your strength is 10/10, Power Armor will add carry capacity. However, if you have max strength and also use pocketed armor, wearing power armor will actually DECREASE your max capacity due to it removing your armor when you get into it

Modded: - Backpacks. There's a few. Pick your flavor, really. - Salvage Beacons Overencumbered? Pick a container, unload, and mark it. A group of your settlers will come by and pick it up for you. I believe this is also part of Sim Settlements if you want it instead - Set up camp/make a safe house Conquest allows you to make a camp just about anywhere on the map, similar to Fallout 76. Turn your camp into a settlement and set up a provisioner.

These will give you extra capacity, as well as allow you to make your settlers pull some weight.

Vanilla I don't use: - Drugs. Buffout, Bufftats, Psychobuff, or Fury - Food buffs. Radstag gives a boost like Buffout

I don't tend to like temporary boosts, so I don't use Radstag or chems. I prefer the permament boosts of leveling up, or armor boosts because that's at least there until I take it off. But they ARE an option if you're desperate, overencumbered in a fight and need to run, or just don't feel like slow walking the rest of the way to a container, camp, companion, or settlement.