I used to see the fat Buddha not only in our home but also in the homes of my friends. In those times when I was young, the fat Buddha is a symbol of luck and prosperity hence people were buying such figurines for display.
When we started traveling abroad, I had the realization that the Buddha is not really fat. In Bangkok, where 90% of Thais are Buddhists, their temples have the Buddha figurines and statues that do not look like the fat Buddha. Even in the Buddhist temples in Hongkong, the Buddha there are not fat. That means the fat Buddha was not for religious purposes.
Do you see a fat Buddha in the public places?