Evolution to store limited Fat
"Wouldn't obese people die faster and clean the gene pool for people who are slim?" 

If your hypothesis is right, the selection for such traits would only have begun in the last 20-30 years ("Worldwide obesity has more than doubled since 1980" http://www.who.int/mediacentre/factsheets/fs311/en/)

Natural selection wouldn't have had time to select against people showing tendency for obesity.

Also, obesity is a lifestyle choice, and not merely predictable by genetic disposition. I could be a "fit" person, but genetically predisposed to obesity.

Look up also genotype vs phenotype for further reading (http://evolution.berkeley.edu/evolibrary/article/genovspheno_01)