c. 1300, wirien, "to slay, kill or injure by biting and shaking the throat" (as a dog or wolf does), from Old English wyrgan "to strangle," from Proto-Germanic *wurgjan (source also of Middle Dutch worghen, Dutch worgen, Old High German wurgen, German würgen "to strangle," Old Norse virgill "rope"), from *wergh-, from PIE root *wer- (2) "to turn, bend."
The "strangle" sense generally was obsolete in English after c. 1600; the figurative meaning "to annoy, bother, vex" is by c. 1400. Meaning "to cause mental distress or trouble" is attested from 1822; intransitive sense of "to feel anxiety or mental trouble" is attested by 1860. Related: Worried; worrier; worrying.
The earliest attested use is figurative of the literal one, which is from the popular medieval entertainment of setting dogs on some ferocious beast to bite and worry it. The verb also in Middle English could mean "put a horse or other domestic beast out to feed or graze," and, of persons, "to eat food," also figuratively "feast the eye" (late 14c.). Compare bait (n.). Related: Baited; baiting.
1580s, "to torture" (trans.), from French agoniser (14c.) or directly from Medieval Latin agonizare "to labor, strive, contend," also "be at the point of death," from Greek agonizesthai "contend in the struggle, contend for victory or a prize" (in reference to physical combat, stage competitions, lawsuits), from agonia "a struggle for victory," originally "a struggle for victory in the games" (see agony). Intransitive sense of "suffer extreme physical pain" is recorded from 1660s; mental sense of "to worry intensely" is from 1853. Related: Agonized; agonizing.
"to attack persistently, worry, pester," 1790, from badger (n.), based on the behavior of the dogs in the medieval sport of badger-baiting, still practiced in late 19c. England as an attraction to low public houses. Related: Badgered; badgering.
A badger is put into a barrel, and one or more dogs are put in to drag him out. When this is effected he is returned to his barrel, to be similarly assailed by a fresh set of dogs. The badger usually makes a most determined and savage resistance. [Century Dictionary]
Old English sorg "grief, regret, trouble, care, pain, anxiety," from Proto-Germanic *sorg- (source also of Old Saxon sorga, Old Norse sorg, Middle Dutch sorghe, Dutch zorg, Old High German soraga, German sorge, Gothic saurga), perhaps from PIE *swergh- "to worry, be sick" (source also of Sanskrit surksati "cares for," Lithuanian sergu, sirgti "to be sick," Old Church Slavonic sraga "sickness," Old Irish serg "sickness"). Not connected etymologically with sore (adj.) or sorry.