Born near Cookstown, Northern Ireland, and educated at the Queen's College, Belfast, Weir was influenced by the Student Volunteer Movement and pledged himself to missionary service in 1898. He arrived in Manchuria in 1899 and served at various centers, including Chaoyang, Kuyushu, and especially Changchun.
After his first wife Eva (Simms) died in 1915, he married fellow missionary Margaret Grills in 1917. Personally humble and self-effacing, Weir was one of the outstanding missionaries of his time. He was interested in evangelism and at the same time opposed to rigid dogma in communicating the gospel. Far more aware than most of his colleagues of the need for a genuinely Chinese church, he worked both for the training of Chinese leadership and for the growth of indigenous church structures.
Besides being responsible for two large districts for much of his missionary career, he had important administrative duties as clerk of the Chinese synod for 27 years and treasurer of the Irish Presbyterian mission. He helped in forming the Church of Christ in China in 1926 and was an influential member of the National Christian Council of China. He died at Changchun in Manchuria.