This paper introduces an adaptive multi-objective MPC for DC-DC converters that resolves the conflict between output voltage and inductor current regulation. The proposed method uses a cost function with a weighting factor that adapts to the output voltage error, enhancing current limiting during large transients while ensuring precise voltage regulation at steady-state. A novel, systematic design methodology for this adaptive weight is presented based on scale analysis. Experimental results on a dc-dc buck converter validate the strategy and its effectiveness.