The Romans understood anxiety as choking. Latin anxius comes from angere, 'to squeeze, to choke, to cause distress', from Proto-Indo-European *h₂enǵʰ- meaning 'tight' or 'narrow'. Worry was not abstract — it was the throat closing.
This physical metaphor runs through the entire word family. Anguish is the same choking distress. Angina pectoris — chest pain from restricted blood flow — uses angere directly. Even anger, through Old Norse angr ('grief, distress'), connects back to the same root: rage as constriction.
German Angst, borrowed into English as a loanword, carries the same etymology but a broader philosophical weight, thanks to Kierkegaard and Heidegger. English anxiety is clinical; German Angst is existential. Both describe the same tightening.
The word entered English directly from Latin in the early 1600s, which is unusual. Most Latinate words in English arrived via French after the Norman Conquest. Anxious skipped that intermediary, perhaps because it was adopted by scholars reading Latin medical and philosophical texts during the Renaissance.