TL;DR: To convert, add or subtract 16 to DCs or contested rolls, multiply/divide distances by twelve, multiply/divide carrying-weights by sixteen, divide torchlight by four or multiply it by three.

In 5e, the smallest size category is tiny but in 3e, there were two below that. Diminuitive, and fine. We wanna cook up some house rules for the Fine size.

If you are Fine (like a few inches tall) and you're doing something in your own world, just do it like a normal human. Humans are like giant kaiju to you. One inch is like a foot to you. If you need to interact with stuff from the human world and your size matters (so str mostly), add 16. For example, opening a bottle your own size is DC 0. Opening a bottle a much bigger size is DC 16.

Distances, an inch is a foot. Divide by twelve. Walking a six mile hex is two hours for a human but three full 8h days if you are fine. Buuut if you're a fairy maybe you can fly as fast as a human walks?

Light sources scale by the inverse square law so if you have torches and lanterns your size, their light is a fourth if you're shining in "human scale", or multiply by three if you're in your own scale. For example, torches in 5e are 20 bright, 20 dim. A Fine sized torch for fairies are instead 5 foot bright, 5 foot dim, either by divide 20 foot by four or by multiplying 20 inches by three, either way you get five feet. Similarly, a human lantern is 30 feet so a Fine lantern is 7.5 feet, which you also can get to by either method.

Carrying stuff, an ounce is a pound. So just divide strength by sixteen. (Twice halved what a Tiny creature can carry.) So an unarmed Fine creature with strength 10 can carry 150 tiny items or three small items like spellscrolls or daggers.