"that with which anything is tied," Old English teag, from Proto-Germanic *taugo (cf. Old Norse taug "tie," tygill "string"), from PIE *deuk- "to pull, to lead" (cf. Old English teon "to draw, pull, drag;" see duke (n.)).
Figurative sense is recorded from 1550s. Meaning "equality between competitors" is first found 1670s, from notion of a connecting link (tie-breaker is recorded from 1961). Sense of "necktie, cravat" first recorded 1761. The railway sense of "transverse sleeper" is from 1857, American English.