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.
"full of zeal" (in the service of a person or cause), 1520s, from Medieval Latin zelosus "full of zeal" (source of Italian zeloso, Spanish celoso), from zelus (see zeal). The sense "fervent, inspired" was earlier in English in jealous (late 14c.), which is the same word but come up through French. Related: Zealously, zealousness.
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Definitions of overzealous from WordNet
marked by excessive enthusiasm for and intense devotion to a cause or idea;