Statues of the Buddha with a round belly come from China. There a round belly is seen as a sign of wisdom, and thus the Buddha was depicted in this way.
There is also a story of a famous and particularly wise Buddhist monk called Budai, who, it was said, also had a round belly. He ministered in China and some think this may have influenced subsequent depictions of the Buddha.
However, it could, of course, be the other way around - Budai may have been described as having a round belly because he was so wise, like the Buddha.