If your bags are overloaded with junk during your Fallout 4 journeys, there are ways to get around your inventory weight limit. One trick should sound very familiar to Elder Scrolls V: Skyrim players.
The first exploit requires a companion. They, like you, can only carry a finite amount of equipment. However, here's how to circumvent it:
1. Drop the excess items you want your companion to carry on the ground.
2. Click on your companion and then on the items on the ground. You'll order them to pick up this equipment.
3. Your companion will grab these items even if they're at their maximum carrying weight. They won't suffer any ill effects from being overburdened.
While it's kind of silly that this bug survived into another Bethesda game. Still, I'm glad it's here. Fallout 4 makes it harder than usual to keep your bags light. The crafting and building systems require you to grab a bunch of junk during your travels so you can convert it back into usable material at workshops. All that garbage adds up really quickly.
One Reddit user also claims you can use severed heads to get around the inventory weight limit. When you decapitate an enemy, the head still counts as a container just like their body. You can dump items into the head and then put the head into your bag to trim a huge amount of weight from your inventory. This also apparently works with other severed limbs as well. If you're worried about losing your fleshbag by accident, you can put another body part at a settlement because it shares the same inventory.
If you're looking for a more honest way to manage your inventory, I'd suggest a couple armor modifications. The lightweight modification reduces the weight of an armor piece while the pocketed modification increases your maximum carrying weight. Both mods are pretty cheap to make, too.
If you're looking for a less honest way, there are always cheat codes. You can simply boost up your Strength so you can carry more gear. Alternately, you could stop picking up junk and merely summon more for yourself when you're back at a workshop.
Fallout 4 launched just a few days ago and players have already found some really useful exploits. For example, you can find out how to get infinite bottlecaps on all platforms here. The one catch with exploits, though, is that Bethesda could patch them out very soon.