OD&D/AD&D 1st edition: 1 in 10 million jewels
In 1st edition, gemstones can get extremely high value for very little weight. Encumbrance in 1st edition is measured in the equivalent encumbrance of a number of coins, or "cn",
Gems have a range in cn of 1-5, but no additional clarifications are given in terms of size or type. As such, we will be assuming 1 cn gems of high value. This converts to 0.1 lbs according to the PHB:
The conversion ratio of gold pieces to pounds of weight is 10 to 1
The most valuable gems are jewels (with a base value of 5,000 gp), and they have a 1 in 10 million chance of reaching 1,000,000 gp in value:
roll a d10 for each stone, and consult the table
1 | Stone increases to next higher base value; roll again ignoring results above 8. Stones above 5,000 gold piece value progress as follows: 10,000 GP, 25,000 GP, 50,000GP, 100,000 GP, 250,000 GP, 500,000 GP, and 1 ,000,000GP- the absolute maximum. No stone may increase beyond 7 places from its initial base value.
With a weight of 0.1 lbs, and a value of 1,000,000 gp, our gp/lb is 10,000,000 gp
BECMI: very large size, very good quality tristals
BECMI works similarly to OD&D and 1st edition in terms of encumbrance, and once again gems are our best source of value. A gem is 1 cn (which we'll call 0.1 lbs) in encumbrance. While the Rules Cyclopedia clairifies that gems don't weigh 0.1 lbs:
For convenience's sake, all gems have the same encumbrance value: one gem equals 1 cn of encumbrance. This is not so much a function of the gem's weight as of the gem's size and irregular shape, which make it inconvenient for carrying.
...we can use 0.1 lbs as an upper bound. According to that same chapter, the most valuable gem is a tristal:
Corundum, a mineral, is the substance of which rubies and emeralds are made. It may also be found in other colors, rare and usually transparent: golden yellow, deep violet, and brilliant orange. These gems are known as tristals. A tristal may have any value the DM chooses from 1,000 to 100,000 gp, but the average tristal is worth 50,000 gp.
From there, gems can vary in size or quality. A very large size, very good quality gem has a 64x value
With a weight of <0.1 lbs, and a value of 640,000 gp, our gp/lb is >6,400,000 gp
AD&D 2nd Edition: blackslings
The lightest items in 2nd edition are labelled as:
These items weigh little individually. Ten of these weigh one pound.
...so I looked through all four volumes of Encyclopedia Magica where magic item values can be found for items of this weight (no items of greater weight come close to the gp/lb value), and the most valuable of these types of items is a blacksling (p. 1119):
This powerful weapon is a light, wispy black sling, easily concealed amid or beneath clothing. Operating as a sling +3 (no damage bonus), these devices feel slippery. They are hard to snatch or steal... and cannot be use to tie things to creatures.
With a weight of 0.1 lbs, and a value of 90,000 gp, our gp/lb is 900,000 gp
3rd Edition: bracers of relentless might
The most valuable magic items in 3rd edition are epic magic items. While some of them break 5,000,000 gp, none of these are light enough. As such, we get the bracers of relentless might as our best option:
These bracers grant a +12 enhancement bonus to the wearer’s Strength and Constitution. The wearer is treated as two size categories larger than normal (to a maximum of Colossal) for purposes of combat-related opposed checks that apply a modifier based on size...
With a weight of 1 lbs, and a value of 4,384,000 gp, our gp/lb is 4,384,000 gp
4th Edition: Level 30 magic shuriken
Magic items in 4th edition have fixed costs based on the level of the magic item (from 1 to 30). Level 30 magic items have a value of 3,125,000 gp.
As such, we simply have to look for the lightest item that can receive a level 30 enchantment. This turns out to be shuriken (5 of them weigh 0.5 lbs) with either the flaming +6, lightning +6, or perfect hunter's enchantments (from the Player's Handbook I; other books probably have more options):
You can will this weapon to burst into flame.
This weapon crackles with dancing lightning.
Perfect Hunter’s Weapon
This weapon ignores cover and concealment when its magic is
With a weight of 0.1 lbs, and a value of 3,125,000 gp, our gp/lb is 31,250,000 gp
5th Edition: arrows of slaying
We have two options for 5th edition using the magic item costs from the Dungeon Master's Guide. Highly lightweight Very Rare magic items, or somewhat lightweight Legendary magic items. To complete this we get either an arrow of slaying:
An arrow of slaying is a magic weapon meant to slay a particular kind of creature... If a creature belonging to the type, race, or group associated with an arrow of slaying takes damage from the arrow, the creature must make a DC 17 Constitution saving throw, taking an extra 6d10 piercing damage on a failed save, or half as much extra damage on a successful one.
With a weight of 0.05 lbs, and a value of 50,000 gp, our gp/lb is 1,000,000 gp
Note: If you would rule that arrows are consumables, this amount is cut in half. In this case, any Legendary magic item that weighs 1 lb would be equal in value such as a red wizard blade.