The civilizational fault-line that cuts Germany in half has more on-the-ground effects than what type of folk culture the people adopt, or what their religious history has been. It turns out that the stereotype of "fat Germans" or "fat German tourists" is another example of outsiders observing only one half of "Germans," and applying what they see to all of "Germany."
Hilly/mountain country is more suitable for (agro-)pastoralism, while the vast lowland plains can support large-scale agriculture. If the local diet reflects the local subsistence mode, then we'd expect folks in the west and south to rely more on animal products than they do in the north and east, where we would expect grains and other plant crops to play a larger role.
Obesity, and other symptoms of metabolic syndrome, is primarily caused by an overly high amount of carbohydrates in the diet. Digestible carbs are burned as glucose, which is metabolized by insulin. And insulin is the only hormone that locks fat in the fat cells, rather than release fat into the blood to be burned for energy. So, a long-term reliance on a high-carb diet will tend to lead to the symptoms of metabolic syndrome -- not only obesity, but also diabetes, hypertension, insulin resistance, etc.
Metabolic syndrome is a "disease of civilization," a consequence of agriculture.
Now let's look at a map of the prevalence of "overweight" and "obese" people across the various German states (sources cited here). The top one shows the percent of the state that has a BMI between 25 and 30, the bottom one a BMI over 30. White means low, light blue means intermediate, and dark blue means high compared to the national average.
this map), with folks in the hilly/mountain parts being slimmer than the "corn-fed" people from the Plains and Mid-west or deep South.
Combining both categories gives the following ranking from heaviest to slimmest. (Here is a map showing which states are where).
64.4% - Mecklenburg-Vorpommern
64.3% - Saxony-Anhalt
63.5% - Thuringia
62.8% - Brandenburg
61.2% - Lower Saxony
60.7% - Rhineland-Palatinate
59.9% - Saxony
59.3% - Bavaria
59.2% - North Rhine-Westphalia
58.8% - Schleswig-Holstein
57.8% - Hesse
56.9% - Baden-Württemberg
(I omitted the city-states of Berlin, Hamburg, and Bremen because they're urban centers and not representative of the general area around them. Like how D.C. often gets left out of state comparisons in America. I omitted Saarland for the same reason -- in area and population, it's like the three city-states.)
The only major exception to the north/east being the fattest is Schleswig-Holstein. Saxony is not as fat as the rest of the eastern states, but the article says that the obesity rates do not tell the whole story about Saxony. In the nation as a whole, half of obese people also have diabetes, whereas 3/4 of the obese in Saxony do. So for overall metabolic disorders, it is probably not unlike the other eastern states.
The differences are not huge -- not even 10 percentage points between the fattest and slimmest states. Turning percentages into z-scores, we find a 0.2 standard-deviation gap between the top and bottom states.
But those small differences in the average can lead to dramatic differences in the tails of the distribution. For example, the really tubby Germans we see on beaches are probably from the north/east. And lithe people like supermodels are probably going to come from the west/south. Indeed, both Claudia Schiffer and Heidi Klum hail from North Rhine-Westphalia. (In fairness, Tatjana Patitz comes from Hamburg.)
Tacitus said that the Germanic tribes ate mostly meat and milk (being nomadic pastoralists), and that their bodies were large and strong compared to the wheat-eating Romans. In fact, the barbarians truly were taller than the civilized agriculturalists. This was probably due in large part to diet, because among the Romans themselves, their heights showed a high-low-high pattern over time that reflected their reliance on pastoralism-agriculture-pastoralism. Man does not live by bread alone.
Once the Germanic groups who occupied the lowland plains began to use the land more for sedentary agriculture than for grazing their livestock, that set them off on a different evolutionary path. That is only within the last 2000 years, but natural selection can work fast when the pressure is strong. And being thrown into a strange new subsistence mode would definitely qualify.
I wonder how much Viking influence remains in Holstein, whether genetic or cultural. They are pretty slim, and they're world-famous for their local breed of dairy cattle, the Holstein Friesian. So they might not have gotten pulled toward the adaptation to agriculture as strongly as the rest of their northern neighbors, and stayed a bit closer to the nomadic pastoralist roots of the Vikings. But that's just a hunch.