Carry Weight

Carry Weight is a derived statistic in the SPECIAL system.

Fallout, Fallout 2 and Fallout Tactics
Your character will become slower as more weight is put on. When your character reaches the maximum weight, he or she becomes completely weighed down and cannot move until the weight is back under control.
 * $$\text{Initial level}=25+(\text{Strength}\times25)$$

Example: A starting Strength of 5.
 * $$25+(5\times25)=150~\text{lbs}$$

Fallout 3 and Fallout: New Vegas
Movement speed is unaffected by your character's Carry Weight until the weight of items carried exceeds your total carry weight, at which point your character will become overencumbered and unable to run, jump, or fast travel, with the exception of the Long Haul perk in New Vegas.
 * $$\text{Initial level}=150+(\text{Strength}\times10)$$

Example: A starting Strength of 5.
 * $$150+(5\times10)=200~\text{lbs}$$

Fallout 4
Largely similar to Fallout 3, movement speed is unaffected by carry weight unless overencumbered, and are unable to run or fast travel. However, unlike past games, it is possible to jump.
 * $$\text{Carrying capacity}=200+(\text{Strength}*10)$$

Game settings for carrying capacity:
 * fAVDCarryWeightBase = 200
 * fAVDCarryWeightMult = 10

Bugs

 * As of patch 1.6 companions may occasionally arbitrarily gain a much higher carry weight than they would be capable of under any other circumstances. Triggering this can be as simple as repeatedly engaging a trade with the companion, taking items from them, ending the trade, re-initiating a trade and giving items to them until one has determined the bug has occurred or not. Their ability to accept even more items in subsequent trades appears to also be random. This applies to humanoid companions and Dogmeat.
 * Companions will pick up items when commanded to even when overencumbered, making their carry weight essentially unlimited so long as the items are first dropped and the companion is told to pick them up.

Fallout 76
Largely similar to Fallout 4, movement speed is unaffected by carry weight unless overencumbered; you are able to run or fast travel, and can still jump. Fallout 76 differs in that running while overencumbered drains action points like sprinting. After all points are used, the character's movement will then be greatly reduced. The starting carry weight also differs because Strength starts at 1 for each player character.
 * $$\text{Carrying capacity}=155+(\text{Strength}*5)$$

Carry weight is capped to an absolute limit of 1,500 pounds over the player character's current maximum carry weight.

Backpacks
With the introduction of Wild Appalachia, player characters who complete The Order of the Tadpole are able to craft a backpack that provides a tiny ballistic resistance of 1 and +10/+20/+30/+40/+50/+60 carry weight, at levels 1/10/20/30/40/50, respectively.

One out of the five modifications for the backpack provides an extra +10/+20/+30/+40/+50/+60, totaling to +20/+40/+60/+80/+100/+120 carry weight, at the expense of 10/20/30/40/50/60 points of energy and radiation resistance. The rest of the modifications lower the backpack's carry weight down to +5/+10/+15/+20/+25/+30, while giving other benefits.

Weight-related perks
Several perk cards assist in lightening the burden of weight, with higher tier cards reducing more:
 * Strength perks:
 * Bandolier - Ballistic weapon ammo weighs 45%/90% less.
 * Bear Arms - Heavy Guns weigh 30%/60%/90% less.
 * Martial Artist - Your melee weapons weigh 20%/40%/60% less, and you can swing them 10%/20%/30% faster.
 * Ordnance Express - Explosives weigh 30%/60%/90% less.
 * Pack Rat - The weight of all junk items is reduced by 25%/50%/75%.
 * Scattershot - Shotguns now weigh 30%/60%/90% less and you reload them 10%/20%/30% faster.
 * Strong Back - Gain +10/+20/+30/+40 to carry weight.
 * Sturdy Frame - Armor weighs 25%/50% less than normal.
 * Traveling Pharmacy - Weights of all Chems (including Stimpaks) are reduced by 30%/60%/90%.
 * Intelligence perks:
 * Batteries Included - Energy weapon ammo weighs 30%/60%/90% less.
 * Portable Power - All Power Armor parts and chassis weights are reduced by 25%/50%/75%.
 * Agility perks:
 * Packin' Light - Your pistols weigh 25%/50%/75% less.
 * Thru-hiker - Food and drink weights are reduced by 30%/60%/90%.

My stash box
My stash boxes share the same inventory across Appalachia, meaning that any deposited item can be withdrawn from any box, thus objects do not need to necessarily be carried across the map. The boxes can found at railroad stations, Red Rocket truck stops, or placed at any C.A.M.P. or workshop. Weight-related perks do not affect the weights of items inside it.