Would you concede that there's indeed some subtle difference in the meaning of the expressions below, which makes them non-interchangeable without detriment as to meaning:
weep about something
weep at something
weep about something - cry to express one's grief concerning smth.: Even northern ministers present at that meeting conceded that Ironsi seemed genuinely upset by, and wept about the death of his military colleagues.
weep at something - cry in the presence of that which causes the weeping: You regard him as selfish because he doesn't like novels and doesn't weep at a dog's death.