This population-based cohort study investigated the prevalence, potential risk factors, and consequences of birth weight discordance (BWD) among same-sex twins. We retrieved data from the automated system of healthcare utilization databases of Lombardy Region, Northern Italy (2007–2021). BWD was defined as 30% or more disparity in birth weights between the larger and the smaller twin. Multivariate logistic regression was used to analyze the risk factors of BWD in deliveries with same-sex twins. In addition, the distribution of several neonatal outcomes was assessed overall and according to BWD level (i.e., ≤20%, 21–29, and ≥30%). Finally, a stratified analysis by BWD was performed to assess the relationship between assisted reproductive technologies (ART) and neonatal outcomes. We identified 11,096 same-sex twin deliveries; 556 (5.0%) pairs of twins were affected by BWD. Multivariate logistic regression analysis showed that maternal age ≥35 years (OR 1.26, 95% CI [1.05,5.51]), low level of education (OR 1.34, 95% CI [1.05, 1.70]), and ART (OR 1.16, 95% CI [0.94, 1.44], almost significant due to the low power) were independent risk factors for BWD in same-sex twins. Conversely, parity (OR 0.73, 95% CI [0.60, 0.89]) was inversely related. All the adverse outcomes observed were more common among BWD pairs than non-BWD ones. Instead, a protective effect of ART was observed for most neonatal outcomes considered among BWD twins. Our results suggest that conception after ART increases the risk of developing a high disparity between the weights of the two twins. However, the presence of BWD may complicate twin pregnancies, compromising neonatal outcomes, regardless of the modality of conception.