Background: This study aimed to investigate the changes in distinct types of screen time and explore their longitudinal association with children and adolescents’ weight status. Methods: A two-wave longitudinal study was conducted among 2228 children and adolescents (6–19 years) in Shanghai, China, before and during the pandemic. Recreational screen time (watching TV/videos, online gaming, using social media, and browsing webpages), educational screen time (online homework and online class), and BMI were measured using a self-reported questionnaire. Mixed-effects models were constructed to assess the associations between screen time and weight status. Results: The prevalence of overweight and obesity was 20.5% and 10.2% at baseline, respectively. Both recreational and educational screen time increased significantly over two months. While recreational screen time was found to be a risk factor for obesity, it was not the case for educational screen use. Specifically, adolescents who spent more time watching TV/videos had a higher obesity risk (OR = 1.576). No significant associations were found in children. Conclusions: Overweight and obesity were prevalent among children and adolescents in China. Reducing screen-based activities is a promising strategy to prevent unhealthy weight gain in Chinese children and adolescents, while it is necessary to consider the content and distinguish between educational and recreational screen use.