Rapid weight gain in infancy increases the risk of developing obesity early in life and contributes significantly to racial and ethnic disparities in childhood obesity. While maternal perceived stress is associated with childhood obesity, little is known about the impact it has on infant weight gain. Therefore, this study explores the impact of maternal perceived stress on change in weight-for-length (WFL) z-scores and the risk of rapid weight gain in infancy. We conducted a secondary data analysis of the longitudinal Nurture birth cohort (n = 666). Most mothers in the cohort were non-Hispanic/Latinx Black (71.6%). About one-half of mothers had a body mass index (BMI) greater than 25 prior to pregnancy, were unemployed, and had a low income. Most infants in the cohort were born full-term and were of normal weight. Data were collected at 3-, 6-, 9-, and 12-months postpartum. At each assessment, mothers completed the Cohen’s Perceived Stress Scale (PSS), and research assistants weighed and measured each infant. Tertiles were used to compare mothers with high and low perceived stress. A mixed model analysis of repeated measures assessed the associations between baseline perceived stress and the change in infant WFL z-scores over time. Log-binomial models assessed the association between baseline perceived stress and rapid weight gain, defined as a change in WFL z-score > 0.67 standard deviations from three to twelve months. Just under one-half of the infants (47%) experienced rapid weight gain between three and twelve months of age. Birthweight for gestational age (RR = 1.18, 95% CI = 1.08–1.29, p-value = 0.004), gestational age at birth (RR = 1.07, 95% CI = 1.01–1.14, p-value = 0.031), and weeks breastfed (0.99, 95% CI 0.99–1.00, p-value 0.044) were associated with risk of rapid weight gain in unadjusted analyses. WFL z-scores increased significantly over time, with no effect of perceived stress on change in WFL z-score or risk of rapid weight gain. Rapid weight gain in infancy was prevalent in this sample of predominately Black infants in the Southeastern US. We did not find evidence to support the hypothesis that maternal perceived stress influenced the risk of rapid weight gain. More work is needed to identify and assess the risk factors for rapid weight gain in infancy and to understand the role that maternal stress plays in the risk of childhood obesity so that prevention efforts can be targeted.