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late 14c., "set (one's eyes or mind) on something," probably from Old French *fixer, from fixe "fixed," from Latin fixus "fixed, fast, immovable, established, settled," past participle of figere "to fix, fasten," from PIE root *dhigw- "to stick, to fix."
Sense of "fasten, attach" is c.1400; that of "settle, assign" is pre-1500 and evolved into "adjust, arrange" (1660s), then "repair" (1737). Sense of "tamper with" (a fight, a jury, etc.) is 1790. As euphemism for "castrate a pet" it dates from 1930. Related: Fixed; fixedly (1590s); fixing.
"position from which it is difficult to move," 1809, American English, from fix (v.). Meaning "dose of narcotic" is from 1934, shortened from fix-up (1867, originally in reference to liquor).
A date arranged by a third party: not sure if a fix-up is any better than a blind date