Under Wee's direction, UOB expanded its branch network in Singapore and internationally, and further diversified into the finance business, property, insurance, realty, trustee and executor services, lease financing and merchant banking. The bank went public in 1970, and Wee was appointed vice-chairman a year later. In June 1971, UOB acquired 49.8% of the Chung Khiaw Bank, and Wee made the newspaper headlines for sealing the deal for a bank that at the time had a larger asset base and a larger network of branches. The S$22 million deal saw UOB beat more than six rivals to the deal and doubled UOB's size, creating the second largest banking group in Singapore and Malaysia. Wee later named the Chung Khiaw deal as one of his most important, as it marked UOB's take-off into the wider Asian market.
Wee had been appointed chairman of the Nanyang University council in 1970, and he led efforts to modernise the university by updating its curriculum and establishing English as its medium of instruction. After the government merged Nanyang with the University of Singapore in 1980, Wee was appointed to the council of the newly formed National University of Singapore. In 2004, he became pro-chancellor of the Nanyang Technological University (NTU).