Animals are constantly moving and hence they burn out whatever they eat. Hence the animals, mostly in jungles don't become overweight.
However, that is not always true for animals in captivity. Those animals in captivity also tend to be overweight and they need to be exercised or put on a diet to get rid of their excess weight.
Humans, especially those in cities tend to spend more time in inactivity ie no exercise, hence they don't burn the food they consume very efficiently. The excess food tends to accumulate in the form of fat in the human body, and hence they become overweight.
So, the main reason for being overweight is not the fact that one is a human or animal, but whether they are burning the food they consume or not.