I will try to (very) roughly estimate both the cost of obesity and the cost of extra pension paid due to not being obese, so there will be many assumptions and guesses.
Average life expectancy in US is now about 79 years.
Average retirement age is about 63.
=> about 16 years for an average person
Average retirement age income supported by Social Security is about 1300$/month => 15600$/year
Estimated obesity cost is about 600$/year/person:
The medical care costs of obesity in the United States are high. In
2008 dollars, these costs were estimated to be $147 billion. => 460$
The annual nationwide productive costs of obesity obesity-related
absenteeism range between $3.38 billion ($79 per obese individual) and
$6.38 billion ($132 per obese individual)
=> ~600$ / year / individual
However, obesity related costs are much higher due to more expensive comorbidities:
Thompson and colleagues concluded that, over the course of a lifetime,
per-person costs for obesity were similar to those for smoking. (10)
In middle-age men, treatment of five common obesity-related conditions
(stroke, coronary artery disease, diabetes, hypertension, and elevated
cholesterol) resulted in roughly $9,000 to $17,000 higher costs
compared to normal-weight adults.
=> ~13000$ / year / individual
We must also take into account that in the most cases obesity does not imply not getting a pension. Life expectancy is reduced based on obesity degree:
The Oxford University research found that moderate obesity, which is
now common, reduces life expectancy by about 3 years, and that severe
obesity, which is still uncommon, can shorten a person’s life by 10
years. This 10 year loss is equal to the effects of lifelong smoking.
Let's assume an average life expectancy reduction of about 5 years.
So, life expectancy reduction saves the Government about 5 * 15600 = 78000$ / person
On the other hand, there are great expenses related to obesity. Let's assume some 20 years of moderate obesity expenses and some 10 years of comorbidities expenses:
20 * 600 + 10 * 13000 = 142000$ / person
So, there is a clear difference between so called savings and obesity related expenses.
Of course, there are so many explicit and implicit assumptions in the computations above that the figures might not be so different after all. Even so, this is the financial dimension only.