The hormone insulin regulates carbohydrate, fat, and protein metabolism by partitioning ingested calories for either use or storage.
When blood glucose levels rise, usually due to carbohydrates in the diet, the pancreas secretes insulin to partition the glucose out of the bloodstream and into muscle, liver and fat cells. Muscles and the liver store a limited amount of this glucose as glycogen. Once filled, they become insulin resistant, meaning insulin no longer partitions glucose into them.
When all muscles and the liver become insulin resistant, superfluous glucose gets partitioned to fat cells, or adipocytes, through a series of chemical reactions that converts the glucose into triglycerides. Unlike muscle cells, adipocytes typically can store much more fat than muscle cells can store glycogen.
Once the adipocytes do, however, become insulin resistant, the pancreas responds by secreting even more insulin as an attempt to get glucose out of the bloodstream, thus starting a negative feedback loop: increased insulin, insulin resistance, and fat deposits. At this point both obesity and, often, diabetes begin. Moreover, as long as insulin remains high, it acts like a lock preventing these fat deposits from being tapped for energy. If your dog is overweight, this process is why.
That a hormone drives obesity, not the conventionally understood caloric imbalance caused by gluttony and sloth, should not come as any surprise. When a dog is a growing puppy, she is obviously consuming more calories than she is burning: she is growing. Hormones – principally growth hormone – drive this growth. When her adipocytes grow, hormones – principally insulin – drive this growth as well. Hormones regulate all growth. None of this is controverted and can be read in any introductory biochemistry textbook.
Moreover, a growing body of research demonstrates that elevated insulin correlates strongly with many chronic diseases such as cancer, hypothyroidism, diabetes, arthritis, and many others. This indicates that many chronic diseases may be rooted in diet.
In short, hormones drive obesity and may drive many chronic diseases. Anything that raises your dog’s insulin will, at a minimum, likely cause his fat tissue eventually to grow. Carbohydrates do this. Since we already know that dogs are carnivores, replacing carbohydrates in the diet with healthy meat makes biological sense.
 See for example: Weeth, LP, et.al. 2007. “Prevalence of Obese Dogs in a Population of Dogs With Cancer.” American Journal of Veterinary Research. Apr. (68)4: 389-98. (https://www.avma.org/News/Journals/Collections/Documents/ajvr_68_4_389.pdf);
Tvarijonaviciute, A., et. al. 2012. “Obesity-Related Metabolic Dysfunction in Dogs: A Comparison with Human Metabolic Syndrome.” BMC Veterinary Research. Aug. (8): 147-55. (http://bmcvetres.biomedcentral.com/articles/10.1186/1746-6148-8-147147);
Lund, EM, et al. 2007. “Prevalence and Risk Factors for Obesity in Adult Dogs from Private US Veterinary Practices.” International Journal of Applied Research in Veterinary Medicine. 4(2): 177-86. (http://www.jarvm.com/articles/Vol4Iss2/Lund.pdf).