The most obvious problem is that survival in the wild depends on not being either underweight or overweight. A fat animal is slower and less agile than its leaner brethren. Predators would preferentially eat the fatter prey over the harder-to-catch, lean prey. By the same token, fat predators would find it much more difficult to catch lean and swift prey. Body fatness does not always provide a survival advantage, but instead can be a significant disadvantage.
