The compound adjective "three-week-old" is a modern English formation built from native Germanic elements. Its logic is transparently numerical and descriptive, following the common English pattern of combining a number, a unit of time, and the suffix "-old" to denote age or duration. The first element, "three", originates from the ancient Indo-European numeral system, preserved with remarkable consistency in English. The central element, "week", derives from a Germanic root concerning cycles or turns, reflecting its original conception as a repeating period. The final element, "old", evolved from a Proto-Indo-European root associated with growth and maturity, here grammaticalized into a suffix that attaches to time measurements to form adjectives specifying age, paralleling constructions like "centuries-old" or "five-year-old".

Structure: three (numeral) + week (time unit) + old (adjective suffix) - three: From Old English þrīe, þrēo, of Proto-Germanic origin; related to Dutch drie and German drei, from an Indo-European root shared by Latin tres and Greek treis. Functions as a numeral root. - week: From Old English wice, wicu, of Proto-Germanic origin; related to Dutch week and German Woche, from a base probably meaning "sequence, series". Functions as a noun denoting a unit of time. - old: From Old English eald, of Proto-Germanic origin; related to Dutch oud and German alt, from an Indo-European root meaning "grown-up, adult". In this compound, it functions as an adjective-forming suffix indicating age or duration.