capillary

From Latin capillāris, "pertaining to the hair," from capillus, "hair (of the head)," which itself traces back to caput, "head."

The word began as a description of hair itself, then narrowed into a technical term for anything hair-thin, like the tiny vessels that carry blood through the body.

It shares its root with capillus, the Latin word for hair, and further back with caput, the word for head — the same head the hair grows from.