The effect of density ratio on the hydrodynamic interaction between two drops in simple shear flow at finite Reynolds numbers is studied considering the gravity influence. In this study the full Navier-Stokes equations are solved by a finite difference/front tracking method. The interaction of two drops contains approach, collision, and separation. For a range of density ratios, the interaction between deformable drops increases the cross-flow separation of their centres. The distance between the drop centres along the velocity gradient direction increases irreversibly after collision and reaches a new steady-state value after separation. The interaction between drops is affected by the density ratio. As the density ratio increases, the final equilibrium position of drops moves to the higher velocity region and the drop deformation increases. Drop deformation prevents drop coalescence at finite Reynolds numbers; the reduced collision cross-section of the drops allows them to glide past each other. The drops accelerate while sliding over each other. As the density ratio decreases, drops rotate more slowly, and the point at which the drops separate is delayed.