Strengthening of early schooling enhances Equal and Inclusive Education (Sustainable Development Goal 4). Early education protects infant development and learning, especially for children suffering from pathologies and risk factors, such as twin birth weight discordance (BWD). These children—particularly the lighter twin—frequently show disadvantages in their cognitive skills. However, research about this issue is particularly scarce. The aims of this study were to (1) analyze the development of cognitive skills in each type of birth weight discordant twins (heavier and lighter ones) at 18, 21, and 24 months; and (2) discover whether there were differences between the two groups of twins in their cognitive skills. A nomothetic, follow-up, and multidimensional observational design was used. The cognitive skills of 32 birth weight discordant twins were observed while they played at 18, 21, and 24 months. The T-pattern analysis was performed using Thème software (Reykjavík, Iceland) to detect the sequential and temporal structure of infant behavior; indicative of cognitive skills. Results showed: (1) longitudinal intra-group differences in both groups of twins; and (2) some inter-group differences, mainly favoring the heavier twins. These results must be considered for designing early educational practices that allow all twins to be prepared for successful future learning.