He was born in Newport Township, Hants County, Nova Scotia, the son of Benjamin Weir.

Prior to Canadian Confederation in 1867, Wier represented Halifax township from 1851 to 1859 and Lunenburg County from 1859 to 1863 in the colonial Nova Scotia House of Assembly.

After losing his seat in the Nova Scotia election of 1863, he turned his attention to his many business interests.

He was president of the Dartmouth Marine Railway and of the Salt Works Company.

He represented the senatorial division of Nova Scotia until his death in Ottawa at the age of 62.