Using data from the only large-scale randomized controlled trial promoting prolonged exclusive breastfeeding, we study how the intervention affected child health and why. The intervention increased weight-for-age in infancy, with effects persisting through adolescence. We show that treated infants were breastfed more and received less water, juice, and other liquids, resulting in a more calorie-dense diet. A mediation analysis indicates that increased caloric intake explains a large share of the early weight gain, while reduced illness explains little. These findings suggest that, in this setting, the main benefits of breastfeeding promotion for physical growth came from improved nutrition. More broadly, the results highlight that the effects of breastfeeding promotion depend on the local alternatives to breast milk and may differ in settings where infant formula or other more nutritious substitutes are the main alternative.