Dnd Beyond only properly calculates Carrying Capacity for Small/Medium/Large characters. Even though there's options to set a Creature's Size or Carrying Capacity to Tiny or Huge/Large, it never actually properly calculates the Carrying Capacity.

For instance, Goliath's have a feature that sets their Carrying Capacity at Large size despite being Medium creatures. So at 20 Strength, a Goliath would have 600lb Carry Capacity instead of 300lb. But setting that feature to consider their Capacity at Huge instead still leaves it at 600lb even though it should be 1.200lb.

Ideally, there should be a way to Manually set the Carrying Capacity of a creature, but having this bug fixed would help a lot. There are campaigns in which Carrying Capacity is important.

You're correct that using the modifier to set Carrying Capacity to anything beyond Large doesn't increase the carrying capacity beyond what it would be when Large, but Carrying Capacity - Tiny does work properly. The Size modifier doesn't work at all currently. It will be nice to have those at some point.

For my Kobold, size small, it does not work, neither normal nor variant encumberance. Neither does homebrewing a feature to adjust it work, despite there being a carrying capacity modifier with options for all sizes. Trying to override the multiplier by fixed value does not work either, not increasing (tried 2), not in order to fix smaller than medium (where it right away fails by not excepting non-integer [would need 0.5, 0.25]). Same for another of my character, fairy, small.

So Size does not work carrying capacity wise at all atm?

My fault, thought it was 2^-2 to 2^3, but both small and medium are 2^0.

The “Size” Modifier doesn’t adjust carrying capacity, you need the “Carrying Capacity” modifier to adjust carrying capacity. But small creatures have the same varying capacity as medium creatures.