Origins
The word 'tear' (the drop from the eye, not the verb meaning 'to rip') is one of the crown jewels of Indo-European etymology — a word so stable, so universal, and so resistant to replacement that it has survived essentially intact for over six thousand years. It descends from Old English 'tēar' (also 'tæhher' in some dialects), from Proto-Germanic *tahrą, from PIE *dáḱru- (tear, teardrop).
The PIE reconstruction *dáḱru- is supported by an extraordinary array of cognates spanning nearly every branch of the Indo-European family. Greek 'dákry' (δάκρυ) is almost identical to the reconstructed form. Latin 'lacrima' (tear) shows an irregular development — the initial *d- became *l- through a process called dissimilation, and the word was further reshaped by folk etymology (an older form 'dacruma' is attested). Sanskrit 'áśru' reflects the same root with regular Sanskrit sound changes. Lithuanian 'ašara,' Old Irish 'dér,' Welsh 'deigr,' Armenian 'artawsr' — all descend from the same ancestral word. The breadth and consistency of these cognates make *dáḱru- one of the most securely reconstructed words in comparative linguistics.
Why has this word been so resistant to change? Linguists have observed that certain words survive for millennia because they occupy a conceptual niche that is both universal and resistant to cultural innovation. Everyone weeps. Every language needs a word for the liquid that comes from the eyes when one is grieving, in pain, or overwhelmed. There is no technological or social change that makes the concept obsolete, no taboo that forces speakers to replace the word with a euphemism, no metaphorical drift that shifts its meaning. The result is a word that has been passed from parent to child for six thousand years with its meaning perfectly intact.
Proto-Indo-European Roots
The English word has a homophone that causes persistent confusion: 'tear' (the noun, /tɪəɹ/) versus 'tear' (the verb meaning 'to rip,' /tɛəɹ/). These are completely unrelated words. The verb 'tear' comes from Old English 'teran,' from Proto-Germanic *teraną, from PIE *der- (to tear, to split) — a different root with a different meaning. The identical spelling is an accident of English orthographic history.
The learned adjective 'lachrymose' (tearful, given to weeping) comes from Latin 'lacrimōsus,' preserving the Latin form of the PIE root. 'Lachrymatory' — a vessel for collecting tears, supposedly used by Roman mourners — entered English in the seventeenth century, though the archaeological objects so named may not have actually held tears. The compound 'tearjerker' (a sentimental story or film designed to provoke weeping) dates from the early twentieth century, first attested around 1921 in American English.
The phrase 'crocodile tears' (insincere grief) dates from the sixteenth century, based on the ancient belief that crocodiles wept while devouring their prey. The belief is attested from late antiquity and appears in medieval bestiaries.