Objective: Most people maintain almost constant body weight over long time with varying physical activity and food intake. This indicates the existence of a regulation that works well for most individuals. Yet some people develop obesity, indicating that this regulation sometimes fails. The difference between the two situations is typically an energy imbalance of about 1% over a long period of time. Theory: Weight gain increases basal metabolic rate. Weight gain is often associated with a decrease in physical activity, although not to such an extent that it prevents an increase in total energy expenditure and energy intake. Dependent on the precise balance between these effects of weight gain, they may make the body weight unstable and tend to further promote weight gain. With the aim of identifying the thresholds beyond which such self-promoting weight gain may take place, we develop a simple mathematical model of the body as an energy-consuming machine in which the changes in physical activity and food intake are described as feedback effects in addition to the effect of the weight gain on basal metabolic rate. The feedback parameters of the model may differ between individuals and only in some cases do they take values that make weight gain self-promoting. Results: We determine the quantitative conditions under which body weight gain becomes self-promoting. We find that these conditions can easily be met, and that they are so small that they are not observable with currently available techniques. This phenomenon encourages emphasis on even minor changes in food intake and physical activity to abate or stop weight gain.