Etymology
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achy (adj.)

"full of aches, sore, aching," 1875, first recorded in George Eliot's letters, from ache (n.) + -y (2). Middle English had akeful "painful" (early 15c.). Related: Achily; achiness.

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ache (v.)

Middle English aken, from Old English acan "suffer continued pain," from Proto-Germanic *akanan, which is perhaps from a PIE root *ag-es- "fault, guilt," with apparent cognates in Sanskrit and Greek, which itself is perhaps imitative of groaning.

Originally the verb was pronounced "ake," the noun "ache" (as in speak/speech). The noun changed its pronunciation to conform to the verb, but the spelling of both was changed to ache c. 1700 on a false assumption of a Greek origin (specifically Greek akhos "pain, distress," which rather is a distant relation of awe (n.)). Related: Ached; aching.

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sore (adj.)

Old English sar "painful, grievous, aching, sad, wounding," influenced in meaning by Old Norse sarr "sore, wounded," from Proto-Germanic *saira- "suffering, sick, ill" (source also of Old Frisian sar "painful," Middle Dutch seer, Dutch zeer "sore, ache," Old High German ser "painful," Gothic sair "pain, sorrow, travail"), from PIE root *sai- (1) "suffering" (source also of Old Irish saeth "pain, sickness").

Adverbial use (as in sore afraid) is from Old English sare but has mostly died out (replaced by sorely), but remains the main meaning of German cognate sehr "very." Slang meaning "angry, irritated" is first recorded 1738.

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