"You are efficient at arranging your inventory in general. Items with a weight of 2 or less weigh half as much for you." - Pack Rat perk NVStyle.

Requirements:
Main game with all DLCs.
FOSE.
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Mod version: 1.4
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Description:
1.You can take the perk at level 8, with INT 5 and Barter 60.
2. After taking the perk or reloading a save with the perk taken, drop an item/ingest some food (alcohol) or fire a bullet and the weight of the items will be recalculated. Obsolete in version 1.4.
3. Very useful if you carry different types of grenades/mines with you, Scrap Metal for Walter (Megaton), Sugar Bombs for Murphy or junk for Rock-It Launcher.
4. Quest items are not affected.
5. I lowered a bit the skill for Barter (70 -> 60) to alleviate the pain of investing so many skill points into the most useless skill from the game.
6. Only vanilla items <= 2 (weight) will be affected. It is not hard-coded into the engine, it is scripted.
7. Works very well with Jury Rigging Wasteland Iridium Edition and Challenges Perks Traits New Vegas Style mods.
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New in version 1.3
Scripts re-written from scratch. Work even better than before.
New in version 1.4
The weight of the items <= 2 will be automatically recalculated after loading your last save. No longer need to fire a bullet or drop an item.
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Note:
The weight of items <=2 will be cut in half and rounded-up, if you have taken the perk.
2 (before perk) -> 1 (with perk)
1.6 (before perk) -> 0.8 (with perk)
1.5 (before perk) -> 0.8 (with perk) not 0.75.
1 (before perk) -> 0.5 (with perk)
0.6 (before perk) -> 0.3 (with perk)
0.5 (before perk) -> 0.3 (with perk) not 0.25.
...etc.

That's it.
Enjoy.

Credits:
Bethesda/Obsidian
A burden to bear.

Many thanks to:
FOSE - a small function works wonders.
FO3Edit - very useful tool.
Nexus