Educated at Bedales in Hampshire, Weston went on to read an MA degree in English at Edinburgh University. Despite her only scientific qualification being one O level in biology, at the age of 23 Weston decided to re-train as a doctor and attended medical school in London from 1993. She qualified as a doctor in 2000 and became a member of the Royal College of Surgeons in 2003.

In February 2009, Weston's book Direct Red - A Surgeon's Story, a set of 14 short stories chronicling her experiences training and practising as a surgeon, was published by Jonathan Cape. Elizabeth Day wrote in the Observer: "I can't remember reading a book that absorbed me so completely, that was so riveting and yet so exact, that so cherished the beauty of language even when using it to convey the ugliest extremes of disease".

Gabriel Weston is the daughter of former British Ambassador to the UN Sir John Weston. She is married to the eminent Australian consultant vascular physician Alexander ("Ander") Cohen with whom she has two young children and lives in London. She continues to practise as a part-time ENT surgeon.