Taking the Rayleigh-Taylor instability with double interfaces as the research object, the interface coupling effects in the weakly nonlinear regime are studied numerically. The variation of Atwood numbers on the two interfaces and the variation of the thickness between them are taken into consideration. It is shown that, when the Atwood number on the lower interface is small, the amplitude of perturbation growth on the lower interface is positively related with the Atwood number on the upper interface. However, it is negatively related when the Atwood number on the lower interface is large. The above phenomenon is quantitatively studied using an analytical formula and the underlying physical mechanism is presented.