"to deceive, cheat, betray," 1924, perhaps from notion of "to have two at a time." An earlier reference (1922) in a Kentucky criminal case involves a double-cross or betrayal without a romance angle. Related: two-timing (adj.); two-timer.
"of long standing; having the characteristics of former times," 1824, from old + time (n.). Related: Old-timey (1850). Old times "olden days" is from late 14c. Colloquial old-timer "one who has long occupied a given place or condition; one who retains the views and customs of former times" is by 1860.