Old English streccan (transitive and intransitive) "to stretch, spread out, prostrate; reach, extend" (past tense strehte, past participle streht), from Proto-Germanic *strakjanan (source also of Danish strække, Swedish sträcka, Old Frisian strekka, Old High German strecchan, Middle Low German, Middle Dutch, Old High German, German strecken "to stretch, draw out"), perhaps a variant of the root of stark, or else from PIE root *strenk- "tight, narrow; pull tight, twist" (see string (n.)).
Meaning "to extend (the limbs or wings)" is from c. 1200; that of "to lay out for burial" is from early 13c. To stretch (one's) legs "take a walk" is from c. 1600. Meaning "to lengthen by force" first recorded late 14c.; figurative sense of "to enlarge beyond proper limits, exaggerate," is from 1550s. Stretch limo first attested 1973. Stretch marks is attested from 1960. Related: Stretched; stretching.