Against the backdrop of rapid urbanization and climate change, energy burden inequity arises between existing and new residential buildings due to generational differences in building envelopes. This study develops a demand-side energy burden equity assessment framework based on energy simulations of typical existing and new apartments in representative cities across China’s five major climate zones. The framework integrates multi-climate conditions, long-term evolution under different Shared Socioeconomic Pathways, and adaptable retrofit implications. Results indicate that demand-side energy burden inequity is widespread but structurally heterogeneous across climate zones, with the largest disparity observed in heating-dominated regions (up to 95.69 kWh/m² in Harbin). Under future warming, three scaling pathways emerge: convergence in heating-dominated regions (up to −27%), divergence in cooling-dominated and mixed regions (up to +382%), and offsetting effects driven by heating–cooling structural shifts in cold regions (up to −5%). Retrofit analysis shows that combined envelope upgrades achieve substantial inequity reduction (88–152%), though with diminishing marginal returns, while single targeted measures already yield high benefits in cooling-dominated and mild regions (74% and 83%, respectively). The findings provide differentiated and forward-looking evidence to support equity-oriented interventions in urban residential retrofitting and policy design.