Height-for-age (HA) and weight-for-age (WA) of children are standard measures to study the determinants of stunting and short-term underweight. Rather than studying these indicators separately, this paper looks at their interaction and therefore at the dynamics of height and weight. Considering HA a child's health stock and WA nutritional investment, we develop an overlapping generations model. The main features of the model are self-productivity of health stocks and the dynamic complementarity between past health stocks and contemporaneous nutrition. We test the model's predictions on a Senegalese panel of 305 children between 0 and 5 years over three periods. To control for endogeneity and serial correlation we employ different GMM methods. We find evidence of self- productive health stocks and that child health produced at one stage raises the productivity of nutritional inputs at subsequent stages. Our results indicate that child health is quickly depleted and needs constant updating. Simulations based on our estimates show that a positive nutritional shock during the first six months of life is essentially depleted at the age of 2. Consequently, sustainable development and nutrition programs have to be long-term and yield higher returns if they reach babies in the early months of infancy.