The effects from a reduction in obesity should ultimately lead to a reduction in costs, in spite of people living longer for two reasons. (1) Healthier, longer lived people tend to have lower total costs since they tend to be healthy til the end, and (2) they are more productive in life, so there is additional productivity to offset whatever additional costs their longevity entails.
As for my assertion (1), I believe it's borne out by the insurance industry, which routinely charge higher premiums to the obese.