Tweedy was refused a job as a teacher on the grounds that if she became pregnant it would be unpleasant for her students. With the onset of World War II she resolved to tackle the effects of wartime food shortages on children. Her efforts with four other women resulted in the Housewives Petition of 1941, out of which grew the Irish Housewives Committee in 1942, which became the IHA in 1946. Under Tweedy's leadership the IHA incorporated the Irish Women's Citizens Association in 1947, a group founded to lobby for reform of the 1937 Constitution of Ireland which defined (Article 41.2) women as home-makers. The merger "strengthened our feminist convictions" explained Tweedy. The work of the IHA expanded from just consumer rights to advocating for political rights. The organization fought for accessible nutritious food, public health, social welfare, and education for all. She was the official Irish delegate to the United Nations World Conference on Women in 1975. In 1992 she published "A Link in the Chain: The Story of the Irish Housewives Association 1942–1992." In 2003 she donated her papers to the National Archives of Ireland.