I got to wondering about this crucial question while sipping on an eggnog and reading an L.A. Times article about the most and least obese communities in Los Angeles County. The skinniest is Manhattan Beach, south of LAX at only 4% obese. It's popular with NHL players and others who like to run on the beach between zipping to the airport. Manhattan Beach went for Obama in 2008, but until then it had been a rare reliable Republican outpost on the West Side.
The fattest town in L.A. County is Bell Gardens, a 96% Latino inland city, at 36% obese. Bell Gardens consistently votes Democratic.
In general, people in L.A. are not terribly fat by modern American standards. At 6-4 and 200 pounds (which sounds pretty good, because you are used to reading height-weight combinations for broad-shouldered, low-body fat athletes, not for narrow-shouldered pundits), I feel like Gozer the Gozerian reincarnated as the Stay-Puft Marshmallow Man when I waddle down Ventura Blvd.
Much of Democrats' feelings of superiority are tied into the observation that Red States are generally fatter than Blue States. But, that's a lot like the popular Red State - Blue State IQ hoax that went around after the 2004 election: Blacks and Latinos simply aren't considered in the average white Democrat's mental picture of why Democrats are better. Moreover, among whites in Red States, Republicans tend to be better educated and, likely, skinnier.
On the other hand, Republicans are more likely to be married. As comedian Emo noted back in the 1980s: "My sister and her husband just found out they haven't been legally married for the last ten years because the minister who married them was a fraud. It's really sad. Now, she'll have to lose all that weight."
So, it's hard to say for sure. There's probably something in the GSS about this. Joseph Fried's book on Republicans and Democrats says that the weight of evidence suggests that Democrats are a little fatter, but it's probably a pretty close run thing.