I wish that 5e had included an encumbrance variant similar to the one described on Delta's D&D Hotspot:
http://deltasdnd.blogspot.ca/2007/04/encumbrance.html
http://deltasdnd.blogspot.ca/2010/09/stone-encumbrance-detail-example.html
It uses the old English
stone as the unit of measurement, where 1 stone = 14 pounds.
The primary benefit of this is that you are primarily only having to deal with single-digit numbers, which makes calculating encumbrance much quicker and easier.
It also works quite nicely with the default 5e encumbrance rules, where your carrying capacity is 15 times your Strength score. Those numbers are close enough that you could simply state that your carrying capacity is equal to your Strength score. This measurement is intentionally less precise than using pounds, so you can play with the numbers a bit in order to provide greater differentiation within a specific category.
Under the variant encumbrance rules, characters are encumbered at 1/3 of their Strength scores and heavily encumbered at 2/3.
The example values that Delta uses (for OD&D) are:
Plate -- 5 stone
Chain -- 3
Leather -- 2
Shield -- 1
Weapon, heavy -- 1
Weapon, light -- 1 per 3 carried
Misc. Equipment -- 1 (total)
With the addition that tiny items (such as daggers, potions, etc) only count if you're carrying a significant number of them (1 stone per 6 items), and he sets 150 coins to 1 stone.
Jack's Toolbox expands on this
https://jackstoolbox.wordpress.com/2012/05/25/weights-and-measures/
https://jackstoolbox.wordpress.com/2012/05/18/carrying-the-world-on-your-back/
It's definitely less accurate than the standard system, but I think it is far more playable and stands a chance of actually being used in play. I've never seen encumbrance calculated beyond buying initial equipment during character creation.
I'll be trying it out the next time I'm able to run a game (whenever that might be).