Origin and history of outstretch

Middle English strecchen, from Old English streccan (transitive and intransitive) "draw out to full length, spread out, prostrate (oneself);" also "to reach or extend in space" (past tense strehte, past participle streht).

This is 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.)).

The meaning "lay out for burial" is from early 13c. The transitive meaning "extend (the limbs or wings)" is from c. 1200. The meaning "extend or strain too far, impair by stretching" is from early 13c., originally as a method of torture. 

The meanings "pull taut, lengthen or draw out by application of force" also "be continuous to a certain point" are recorded from late 14c.; hence the sense of "extend or cause to reach" between two points, attested by early 15c.

The intransitive sense of "bear extension without breaking, be elastic" is from late 15c. The colloquial meaning "eke out, serve more than intended" is by 1923.

The figurative sense of "enlarge beyond proper limits, exaggerate," is from 1550s. The slang meaning "to hang" is by 1570s, perhaps from the sense in stretch a rope (or halter) "be hanged" (1590s). Related: Stretched; stretching.

To stretch (one's) legs "take a walk" is from c. 1600. Stretch limo is attested by 1973. Stretch mark "linear mark on skin left by distention," especially in pregnancy, is attested from 1960.

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]