Socio-economic development (SED) remains a critical priority for policymakers aiming to foster inclusive growth and drive national progress. This study presents a comprehensive multi-criteria assessment of regional SED across 16 Indian states, focusing on the influence of innovation (INV) performance and foreign direct investment (FDI) on achieving sustainable development goals (SDGs). A new multi-criteria decision-making (MCDM) method, called Preference using Root Value based on Aggregated Normalisations (PROVAN), is introduced in this paper to enhance decision accuracy by integrating five different normalization techniques. Criteria weights are determined using an extended version of Weights by ENvelope and SLOpe (WENSLO) method, which incorporates multiple normalization strategies to improve robustness. The evaluation considers nine SED and seven INV criteria derived from secondary data sources. The causal relationships are statistically analyzed using Somer's δ test, and the model's reliability is confirmed through comparative and sensitivity analyses. Results reveal that Maharashtra emerges as the top-performing state in both SED (1.5572) and INV (1.5473), followed by Tamil Nadu and Karnataka, indicating strong performance across socio-economic and innovation indicators. The findings highlight significant inter-state disparities and confirm that states with stronger innovation capabilities tend to achieve better socio-economic outcomes. FDI is shown to positively influence sustainable economic development, reinforcing the strategic importance of attracting capital to advance SDGs. The proposed PROVAN-WENSLO framework offers a robust and adaptable tool for regional development planning and policy formulation.