c. 1600, "part or character one takes," from French rôle "part played by a person in life," literally "roll" (of paper) on which an actor's part is written, from Old French rolle (see roll (n.)). Not originally in English with direct reference to actors and the stage, but figurative of them. The meaning "any conspicuous function performed characteristically by someone" is by 1875. In the social psychology sense is from 1913. Role model, one taken by others as a model in performance of some role, is attested by 1957.
"to chase, set upon" (as in command sick him!), 1845, a dialectal variant of seek. As it was an imperative to incite a dog to attack a person or animal, it came to mean "cause to pursue." Related: Sicked; sicking.
Middle English sik, from Old English seoc "ill, unwell, diseased, feeble, weak; corrupt; sad, troubled, deeply affected by strong feeling," from Proto-Germanic *seuka-, which is of uncertain origin.
It is the general Germanic word (compare Old Norse sjukr, Danish syg, Old Saxon siok, Old Frisian siak, Middle Dutch siec, Dutch ziek, Old High German sioh, Gothic siuks "sick, ill"), but in German and Dutch it was displaced by krank "weak, slim," probably via the notion of "twisted, bent" (see crank (n.)).
The restricted meaning of English sick, "having an inclination to vomit, affected with nausea," is from 1610s. By c. 1200 as "distressed emotionally by grief, anger, etc.; physically ill through emotional distress. The sense of "tired or weary (of something), disgusted from satiety" is from 1590s; the figurative phrase sick and tired of is attested from 1783. To worry (oneself) sick is by 1952.
The modern colloquial meaning "mentally twisted" is by 1955, a revival of the word's use in this sense from 1550s (the sense of "spiritually or morally corrupt" was in Old English, which also had seocmod "infirm of mind"). Sick joke is attested by 1958.
"those who are sick, persons suffering from illness," Old English seoce, from the source of sick (adj.). Colloquial sense of "vomited matter" is by 1959.