This largely has to do with the genetic and evolutionary differences between bears and humans. In evolutionary terms, the group to which primates belong, Archonta, and the group to which bears belong, Ferae, diverged over 100 million years ago. Even though we may think of bears and being close relatives due to being fellow mammals, they've had a very, very long time to make their differences significant.
Bears hibernate,although the exact definition of "hibernation" is a bit contentious, and some argue that bears do not truly hibernate in the same sense as other animals. What is certain is that bears go through an extended period, 100 days or more in winter, where their metabolic activity plummets. They neither eat nor produce waste during this time. Cubs are also born and nursed during this period. Naturally, the body continues to use calories in order to maintain its basic functions, and so the bear goes through another phase, in autumn, called hyperphagia ("super-eating") in order to store up enough energy in the form of fat for this prolonged fast. The bear can nearly double its weight during this time, at a rate of up to four pounds a day.
It certainly seems intuitive that a human doubling its weight in the course of a few weeks would be foolish and dangerous, and indeed it would; the underlying reason for this is that humans have a different series of metabolic controls selected by our evolutionary history.
For bears, hyperphagia and the preparation for a winter fast have, presumably, been in place for millions of years. Bears with a favorable metabolism, one which allows the animal to store lots of energy as fat, and then burn that fat almost exclusively, would be highly selected for. In contrast, humans have only had a few thousand years, or even a few decades, during which we had the abundance of food that would make doubling our body weight possible, let alone a medical question. Humans have never hibernated, nor practiced hyperphagia, and thus what has become normal to the bear is extreme to us. If, on the other hand, we began practicing hyperphagia and then fasting for months, humans with the appropriate metabolism would be highly selected for, and in a few million years we'd have bear-like humans doubling their weight every autumn.
That said, the human metabolism has an enormous degree of plasticity. We are capable of ingesting huge amounts of food, and fasting for prolonged periods, with little change in our performance. This is, again, due to our evolutionary origin as foragers, scavengers and hunters; a predictable intake of X calories per day was simply not in the human experience, and so our bodies developed metabolisms with a lot of built-in buffers and fallbacks that allowed us to function consistently through wildly different calorie intake periods.
Consider, also, that weight-related sicknesses in humans tend to reveal themselves in the long term, and only when that weight is consistently maintained.
Bears can gain weight in the winter and remain healthy because they hibernate. Hibernation is what bears and some other animals do in order to survive the winter's food shortage. In order to hibernate, a bear must store their body fat and then use it slowly over the time they are inactive.
During this time, the bear’s fat cells break down and supply them with water and calories. Muscle and organ tissues also break down and supply protein. Human's do the same thing, but the difference is that humans cannot restore muscle and organ tissue, however, bears can. Bears can simply use urea, a part of urine that is made while tissues breakdown, and they use the nitrogen supplied in the urea to build new proteins. I think that's pretty cool!
From an evolutionary standpoint, bears are much better equipped for hybernating than we are. Bears developed methods for surviving winters without a food source and this included gaining summer weight. Their metabolisms have adapted to rapidly gaining and loosing large amounts of weight. The human metabolism is simply not cut out for this. We circumvented food shortages by storing fat for long term use whenever food was available; hence, why it is so difficult for humans to loose belly fat.