In 2004, Weeks was nominated in the Most Popular Newcomer category at the National Television Awards.
Her acting career began with the Juvenile lead in a television series, an adaptation of Anne Fine's Goggle-Eyes (1993), alongside her sister Perdita. Since then she has appeared in many programmes, including the children's series The Wild House and the long-running series Midsomer Murders and Poirot. In 1997 Honeysuckle and Perdita were both in Catherine Cookson's The Rag Nymph, wherein Perdita played the younger version of her sister's character. Her film roles include Annie Ridd in Lorna Doone (2000) and Sarah in My Brother Tom (2001). She starred in The Bill in 2009 as Julie Nowak.
She has recently starred in The Five, created by bestselling thriller Writer Harlan Coben. She is currently best known for her parts in three television series: Close Relations (1998), Ladies & Their Gentlemen (2002–2006), and Foyle's War (2002–2010, 2013, 2015). In the last, a BAFTA Award–winning detective series set in Hastings during and just after World War II, she starred opposite Michael Kitchen. In 2007, Weeks starred in The Inspector Lynley Mysteries as Tania Thompson, a character based on the Canadian serial killer Karla Homolka. In 2008, she appeared as Harriet Pringle in the Radio 4 adaptation of Fortunes of War. In 2012, she played a small part as Mrs Beeton in an episode of the BBC educational programme The Charles Dickens Show.
Weeks was engaged to the poet and musician Anno Birkin for a short period before his death, at age 20, in a car crash in Italy in 2001. She married hypnotherapist Lorne Stormonth-Darling in an impromptu Buddhist wedding ceremony while on holiday in the Himalayas in 2005, followed by a London wedding in July 2007. The couple have one child, Wade, born in 2011, and live in Petworth.
In 2004, Weeks was nominated in the Most Popular Newcomer category at the National Television Awards.
In early 2010, she appeared as "Sarah Prentice" in a production of the Agatha Christie play A Daughter's A Daughter at London's Trafalgar Studios. Later that year, Weeks appeared as Eliza Doolittle in a production of Pygmalion at the Chichester Festival Theatre in West Sussex.
She starred in the UK premiere of Melanie Marnich's play These Shining Lives from 8 May to 9 June 2013.
In August 2015, Weeks was caught speeding on the A3 in south-west London. It later emerged that she was already banned from driving under the totting-up scheme (due to points violations), and in early 2016 was ordered to wear an electronic tag as a consequence when the court imposed a four-week night time curfew on her.
In July 2016, it was reported that Weeks had gone missing, with relatives said to be concerned for her welfare. However, she was later found safe and well and remained with police late that night before being returned to West Sussex.
