"fluid drop from the eye," Old English tear "tear, drop, nectar, what is distilled in drops," from earlier teahor, tæhher, from Proto-Germanic *tahr-, *tagr- (source also of Old Norse, Old Frisian tar, Old High German zahar, German Zähre, Gothic tagr "tear"), from PIE *dakru- (source also of Latin lacrima, Old Latin dacrima, Irish der, Welsh deigr, Greek dakryma).
To be in tears "weeping" is from 1550s. Tear gas is so called by 1917.