The assessment of Positive Energy Districts requires multi-criteria frameworks able to integrate energy performance with environmental, mobility, governance, social and economic dimensions. However, their reliability depends not only on the selected indicators, but also on the weighting structure used to aggregate heterogeneous criteria into a final rating outcome. This study evaluates the robustness of an SDG-inspired rating system for district-scale sustainability assessment through a scenario-based weight-sensitivity analysis. The rating system was developed to support sustainable urban renovation pathways and Positive Energy District planning. It combines 3 mandatory prerequisites with 42 scored credits organised into six categories: energy, environment, mobility, governance, social and economic value. The credits include quantitative standard, quantitative inverted, binary performance-based and binary document-based indicators, allowing technical performance, implementation outcomes and planning requirements to be assessed within a common scoring structure. The methodological contribution consists of testing whether the final score and classification remain stable under different weighting assumptions. An equal-weighting benchmark is compared with two preference-based schemes: a stakeholder-derived scheme, reflecting local priorities and an expert-based scheme, reflecting technical judgements on the relative importance of categories and credits. Variations in total score, category contributions and credit-level influence are examined to identify the components that most affect the final classification. The approach is applied to the Municipality of Monreale, Italy, as a pilot case study to test the framework at local scale and examine how context-specific priorities influence the rating outcome. The results distinguish stable assessment components from those more dependent on subjective, methodological or policy-driven assumptions. This supports the refinement of categories and credits requiring stronger justification, clearer thresholds or stakeholder validation. By applying weight-sensitivity analysis to an SDG-inspired district rating system, the study moves beyond static scoring and provides a basis for interpreting rating outcomes as decision-support evidence. The proposed approach supports sustainable renovation prioritisation, improves assessment transparency and strengthens the use of rating systems in local planning processes.