The phrase gained popularity in the vernacular of the Old West, where it is seldom used without the prefix “plumb”, as in, “Diggin' in that gol' danged gold mine has left me plumb tuckered out!” And since plumb means “whole or entire”, it just amplifies the meaning of being tired to mean “completely worn out”.

Why do we say plumb tuckered out?

When you ate, you tucked food away. By the 1830s, New Englanders had begun comparing the wrinkled and drawn appearance of overworked and undernourished horses and dogs to the appearance of tucked cloth, and they were said to be "tuckered.” Inevitably, the word "tuckered” came to be applied to people who were exhausted.

What does plumb worn out mean?

also plum Informal Utterly; completely: plumb worn out.