Drug repurposing offers an efficient strategy to identify new uses for existing medications, accelerating the transition from research to clinical practice. In this context, observational studies can serve as a valuable alternative to clinical trials, although they face challenges in disentangling causal relationships from mere correlations. For this reason, this study proposes leveraging observational data for drug repurposing by integrating causal inference within a functional data analysis framework. Using UK Biobank data, we investigate the potential of repurposing metformin, a widely used and cost-effective diabetes medication, for treating kidney disease. Moving beyond traditional cross-sectional analyses, we focus on functional outcomes derived from longitudinal measurements instead of single-timepoint diagnoses. We use a weighting approach to control for measurable confounding factors and construct a pseudo-population to estimate the causal association of the treatment on functional outcomes, applying a weighted functional-on-scalar modelling approach. Our findings suggest a positive effect of metformin on kidney function, supporting its potential role as a renoprotective factor and providing a foundation for future clinical trials. Our methodological approach enables robust causal effect estimation with longitudinal observational data, addressing limitations of traditional study designs and enhancing the ability to infer causal treatment effects on functional outcomes.