Size for liability of carrying oil is to anoint a small limb. There is a dispute whether this refers to a small limb or an adult or even the small limb of a baby. (Gemara favors the second severe interpretation)

When the rabbis set the sizes for liability, the used the common usage of the item. If two uses are common, then their size is stringently applied to the smaller size.

The size for water is not a Reviis, even though water is commonly drunk. It is based on the size used for healing, (in an eye plaster). This is either only in the Galil where water is consistently used for healing, or bc water is just the best liquid to use in the eye plaster.

Size for blood is a dispute- either a Reviis or the amount to apply to an age (heal a speck protruding from the eye). They would apply blood from a hen. Blood for a mole was used for cataract.

Waste waters size is a reviis. It could be used to knead clay. Clay itself is a small size of forming hole around opening of crucible, but one wouldn’t bother just kneading clay that size so the waste water has a larger size to knead a lot of clay.

Size of rope is enough to make handle for basket. But for a reed it’s smaller size to make a hanging loop to hold sifter. (One doesn’t use ropes for this bc the coarse ropes may cut it into the kli.)

Size for paper is based on taking enough to write a tax collectors receipt. But erased paper that is not fit for writing is size to wrap around a flask. Hides size is big enough to make amulet. Parchment the size to write parsha of shema yisroel. Ink is the amount to write two letters.

Blank papers size is to write tax collectors receipt. The receipt had two extra large letters written on it, which is equivalent to two regular letters and a margin to hold the document.

Someone who Carries a tax receipt is liable. After they have already shown it to tax collector, it’s a dispute. Tanna Kamma says they are exempt bc it has no real purpose, while r Yehuda says they are obligated bc it can be used to show to additional tax collectors or to verify that indeed it was paid, or just to prove that he’s a person who pays taxes.