How much excess weight a given individual carries on their body and how long they have carried that excess weight is most definitely one of those pertinent factors affecting lifespans for individuals. While there are all sorts of studies dealing with one's weight, one's Body Mass Index (BMI), age, health, and various other factors, scientific studies aren't always able to clearly see through all of the various and myriad factors to come to definitive conclusions.
Yet, because it is well accepted that excess weight carries with it the higher risk of heart disease, gout, stroke, diabetes, higher blood pressure, the wear and tear of excess body weight on body parts, as well as often contributing to mental depression, in addition to many other ill health factors, quite clearly, all of this indicates that excess body weight is not healthy, and clearly is detrimental to general health.
In order for anyone to live to a very old age, they are almost without exception, going to have to lead a life of general moderation, as well as making sensible decisions in regards to their diet, exercise, and state-of-mind. That is to say, those that do the opposite, and have lead lives of immoderation, poor dietary choices, failure to exercise, and have minds that are discombobulated or stressed out, are going to see that those character traits and character failings will, if done long enough, and persistently enough, take their inevitable toll upon the physical body.
Again, it is very important to note that obese people suffer a much higher percentage of debilitating diseases and illnesses that can be either directly applicable to that excess weight or indirectly be a factor from that excess weight. This means, rather obviously, that those that are obese, are not going to be the ones that are going to live exceedingly long natural lives. All of this makes eminent sense, for when the body is physically overtaxed day in and day out, for years upon years, then the result will often be a body that wears out and has more repairs then a body that lives stress free.
While there are all sorts of theories and reasons that have been given as to why mankind has within such a short period of time seen the incidence of obesity increase at rates, previously unknown, the most obvious reason is that more and more people are consuming more calories than they need to actually consume to maintain their body weight and therefore the consequence of having done so is the increase in body weight. This increase in body weight has negative consequences demonstrated by the higher incidence of certain diseases and ailments that obese people have, without even taking into consideration, the lower quality of life, many obese people suffer from.
The real reason why there aren't any really old people that are obese is that obesity in and of itself, is not the natural state of what a human body is conditioned to be at. For those that don't believe that this is so, they should take the time to look around and to observe the animals that live within the natural domains of the animal world, and in particular, those animals that lived with a minimal amount of interference from humanity and they will soon observe that there are no obese animals, and the closest thing to obesity in the wild kingdom is those animals that must bulk up in order to hibernate, during the bleak winter season. Human beings on the other hand, do not hibernate, and obesity clearly cuts down on their lifespan.