After aging, the adhesiveness of asphalt deteriorates, leading to a reduction in the durability of asphalt mixtures and affecting the service life of asphalt pavements. To enhance the anti-aging performance of asphalt, this study employed the method of melt blending to prepare three types of modified asphalt: graphene/SBS modified asphalt (G/SBSMA), crumb rubber/SBS modified asphalt (CR/SBSMA), and petroleum resin/SBS modified asphalt (PR/SBSMA). Different dosages of the three types of modified asphalt were tested for changes in conventional performance indicators. The optimal dosages of graphene, crumb rubber, and C9 petroleum resin were determined to be 2%, 15%, and 5%, respectively. Based on the theory of surface free energy, the effects of anti-aging agents on the microscopic properties of SBS modified asphalt before and after aging were analyzed using the three-liquid method. The mechanisms of strength attenuation at the asphalt–aggregate interface under water exposure and aging were revealed. The results showed that with the increase of aging gradient, the asphalt-aggregate biphasic system became more active. The cohesive energy and peel energy of SBS modified asphalt increased continuously, while the adhesive energy decreased continuously, leading to a decrease in the energy ratio parameter. Resin-based anti-aging agents exhibited the most significant improvement in asphalt adhesion performance, while graphene demonstrated a more stable enhancement in asphalt’s water stability during the aging stage.