Origins
The preposition 'at' is one of the shortest and most frequently used words in English, expressing location ('at home'), time ('at noon'), direction ('aim at'), and state ('at peace'). Its etymology connects it to one of the most productive prefixes in the English vocabulary.
It descends from Old English 'æt' (at, near, by, in), from Proto-Germanic *at (at, to, near), from PIE *h₂ed (at, near, to). The word has been remarkably stable across its history — the phonological form has barely changed in six thousand years, and the core meaning of 'proximate to a point' has remained constant.
The most important cognate is Latin 'ad' (to, toward, at), which is the same PIE word preserved in the Italic branch. While the native English preposition 'at' remained a simple function word, the Latin cognate 'ad' became one of the most productive prefixes in the language through centuries of Latin and French borrowings. The prefix 'ad-' (often assimilated to 'ac-,' 'af-,' 'ag-,' 'al-,' 'an-,' 'ap-,' 'ar-,' 'as-,' 'at-' before certain consonants) appears in hundreds of English words.
Latin Roots
'Add' is from Latin 'addere' (to give to, to put to — ad + dare). 'Adapt' is 'ad-aptare' (to fit to). 'Admit' is 'ad-mittere' (to send to, let in). 'Adopt' is 'ad-optare' (to choose toward). 'Advent' is 'ad-ventus' (a coming-to). 'Adventure' is 'ad-ventura' (things about to come-to). 'Adverse' is 'ad-versus' (turned toward, hence against). 'Advertise' is 'ad-vertere' (to turn toward). 'Advice' is 'ad-visum' (according to what is seen — a looking-to). 'Advocate' is 'ad-vocatus' (one called to — a person summoned to speak for another). In every case, the 'ad-' prefix carries the same meaning as the English preposition 'at/to': direction toward a point.
Old Norse 'at' is the direct Germanic cognate and is the source of the modern Scandinavian prepositions: Danish 'at' and Swedish 'att' (used as an infinitive marker, like English 'to'). Old High German 'az' (at) is another cognate, though Modern German replaced it with other prepositions.
The @ symbol, universally used in email addresses, is called the 'at sign' in English because it was originally a scribal abbreviation in commercial documents meaning 'at the rate of' (as in '10 items @ $5 each'). The symbol's name varies dramatically across languages: Spanish 'arroba' (from an Arabic unit of weight), German 'Klammeraffe' (clinging monkey), Italian 'chiocciola' (snail), and Danish 'snabel-a' (elephant-trunk a) — each culture seeing a different shape in the same curving glyph.