This is the widely accepted theory but it doesn't explain everything. For example, lab animals have actually gotten fatter over time as well, and they are eating carefully measured diets and living in controlled conditions.

Diets are also not effective at losing weight. People rarely stay on them, and a fat person must eat significantly fewer calories, not just the same amount, than a normal person to maintain a healthy weight. Their metabolisms resemble those of starving people, the body desperately trying to return itself to it's "normal" weight.

Likewise normal people fed lots of food to become fat, quickly return to their previous weight after they stop. Genetic studies find obesity is more heritable than nearly any other condition including mental illness, breast cancer, and heart disease. It also appears to be affected by epigenetics. If your grandmother was starving you have a higher probability of becoming obese.