From where did the phrase come?
One source says ‘tucker’ is a colloquial New England word, coined in the early 19th century, meaning ‘become weary’ and which ultimately derives from the Old English verb ‘tuck’, meaning ‘punish; torment.’
However, I believe the more likely answer comes from wordorigins.org, which says the phrase comes from the verb to tuck, meaning to draw in. It’s a reference to the flanks of an animal being drawn in from malnutrition or exhaustion.According to that source, the term began its life as a New England regionalism in the mid-19th century. From the c.1840 Story of Bee Tree: “I’m clear tuckered out with these young ones.” Bartlett’s 1848 Dictionary of Americanisms uses this example: “I guess the Queen don’t do her eating very airly; for we sot and sot and waited for her, till we got eenamost tuckered out.”—N.Y. Family Comp.