c. 1200, "to spread throughout, spread over, cover over," from over- + spread (v.). Related: Overspread (past tense); overspreading. Old English had ofersprædan "to overlay, cover," and compare German überspreiten, Dutch overspreiden.
word-forming element meaning variously "above; highest; across; higher in power or authority; too much; above normal; outer; beyond in time, too long," from Old English ofer (from PIE root *uper "over"). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."
In some of its uses, moreover, over is a movable element, which can be prefixed at will to almost any verb or adjective of suitable sense, as freely as an adjective can be placed before a substantive or an adverb before an adjective. [OED]
Among the old words not now existing are Old English oferlufu (Middle English oferlufe), literally "over-love," hence "excessive or immoderate love." Over- in Middle English also could carry a sense of "too little, below normal," as in over-lyght "of too little weight" (c. 1400), overlitel "too small" (mid-14c.), overshort, etc.
c. 1200, "to stretch out, to lay out; diffuse, disseminate" (transitive), also "to advance over a wide area" (intransitive); probably from Old English sprædan "to spread, stretch forth, extend" (especially in tosprædan "to spread out," and gesprædung "spreading"), from Proto-Germanic *spreit- (source also of Danish sprede, Old Swedish spreda, Middle Dutch spreiden, Old High German and German spreiten "to spread"), extended form of PIE root *sper- (4) "to strew" (see sprout (v.)).
Reflexive sense of "to be outspread" is from c. 1300; that of "to extend, expand" is attested from mid-14c. Transitive sense of "make (something) wide" is from late 14c. As an adjective from 1510s. Related: Spreading.
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Harper, D. (n.d.). Etymology of overspread. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/overspread