Wei was born in Sheng County, Zhejiang Province, China. He received his B.E. in electrical engineering from Shanghai Jiao Tong University in 1936. In 1942, during World War II, he went to the United States. After the war, he became a successful entrepreneur in the shipping industry.

In 1965, Wei invented the China bidding system, later called the Precision Club bidding system. But since he was not an expert at that time, his system did not attract much attention from the bridge community. This remained the case until the Republic of China team, that was trained and led by Wei, finished as runner-up in the 1969 Bermuda Bowl world team championship, in the process beating the strong North America team. The fact they were also finalists in the same championship the following year made Wei an outstanding figure in the world of bridge.

After that, the Italian Blue Team also adopted the Precision Club bidding system and kept their dominant status for nearly 20 years. The great success of the system began a wave of strong club systems all over the world.