Sorry
Old English sārig ‘pained, distressed’, of West Germanic origin, from the base of the noun sore. The shortening of the root vowel has given the word an apparent connection with the unrelated sorrow.
wiktionary
From Middle English sory, from Old English sāriġ(“feeling or expressing grief, sorry, grieved, sorrowful, sad, mournful, bitter”), from Proto-West Germanic *sairag, from Proto-Germanic *sairagaz(“sad”), from Proto-Indo-European *sayǝw-(“hard, rough, painful”). Cognate with Scots sairie(“sad, grieved”), Saterland Frisian seerich(“sore, inflamed”), West Frisian searich(“sad, sorry”), Low German serig(“sick, scabby”), German dialectal sehrig(“sore, sad, painful”), Swedish sårig. More at sore.
etymonline
sorry (adj.)
Old English sarig "distressed, grieved, full of sorrow" (not found in the physical sense of "sore"), from Proto-Germanic *sairiga- "painful" (source also of Old Saxon serag, Middle Dutch seerigh "sore; sad, sorry," Dutch zeerig "sore, full of sores," Old High German serag, Swedish sårig "sore, full of sores"), from *sairaz "pain" (physical and mental); related to *saira- "suffering, sick, ill" (see sore (adj.)). Meaning "wretched, worthless, poor" first recorded mid-13c. Spelling shift from -a- to -o- by influence of sorrow. Apologetic sense (short for I'm sorry) is attested from 1834; phrase sorry about that popularized 1960s by U.S. TV show "Get Smart." Related: Sorrily; sorriness.
