Regarding body mass index (BMI; kg/m2) and mortality, two well established observations are (1) there is a U‐shaped (i.e., concave) association ‐ people with intermediate BMIs tend to outlive people with unusually high or low BMIs; and (2) The nadirs of these curves tend to increase monotonically with age. Whether these associations represent the true shape of the causal effects of BMI remain subject to debate and inquiry. Multiple hypotheses have been advanced to explain either of these two observations. Here we introduce a new hypothesis that may explain both phenomena, by drawing on the so‐called obesity paradox. We evaluate the plausibility that the concave relation and the increase in the nadir with age are mathematical consequences of the relationships among age, BMI, and disease; and mortality as a function of the prior two variables.We incorporate a hypothetical relationship between BMI and disease risk into the Weibull function, F(t) = exp(−λtk), to model the probability of an individual to survive until age t, with a given BMI; by replacing the constant λ with a function of age and BMI, that represents the effects of these two variables on disease and mortality. The resulting function can be viewed as a survival curve that now depends on both BMI and age. We consider the behavior of this survival curve as the individual's BMI varies, while holding t constant, to find the optimal BMI at age t. We then consider the behavior of the optimal BMI for an individual as age increases. In particular, we establish that under the assumptions of our model, the optimal BMI at age t increases as a function of t.