"speed-increasing gear in an automobile," 1929, from over- + drive (n.). Earlier it was a transitive verb, "to drive too hard, work to exhaustion," Old English oferdrifan.
"delayed or withheld beyond the usual or assigned time," 1845 of unpaid bills, 1890 of unreturned library books, 1970 of menstruation, from over- + due (adj.).
"to eat too much," 1590s, from over- + eat (v.). Related: Overate; overeating. Old English had oferæt (n.) "gluttony;" oferæte (adj.) "gluttonous, excessive eating."
also over-exposure, "excessive exposure; an excess of exposure," 1834 in reference to cleavage in women's dress; 1855 in photography, from over- + exposure. Figurative sense, in reference to celebrity, is attested from 1969.