Old English werian "to clothe, put on, cover up," from Proto-Germanic *wasīn- (source also of Old Norse verja, Old High German werian, Gothic gawasjan "to clothe"), from PIE *wos-eyo-, suffixed form of *wes- (2) "to clothe," extended form of root *eu- "to dress."
The Germanic forms "were homonyms of the vb. for 'prevent, ward off, protect' (Goth. warjan, O.E. werian, etc.), and this was prob. a factor in their early displacement in most of the Gmc. languages" [Buck]. It shifted from a weak verb (past tense and past participle wered) to a strong one (past tense wore, past participle worn) in 14c. on analogy of rhyming strong verbs such as bear and tear. Secondary sense of "use up, gradually damage" (late 13c.) is from effect of continued use on clothes. To wear down (transitive) "overcome by steady force" is from 1843. To wear off "diminish by attrition or use" is from 1690s.
"action of wearing" (clothes), mid-15c., from wear (v.). Meaning "what one wears" is 1560s. To be the worse for wear is attested from 1782; noun phrase wear and tear is first recorded 1660s, implying the sense "process of being degraded by use."