In order to discuss the stability and interaction of optical fiber solitons in application devices, linearly coupled nonlinear Schrdinger (NLS) equations with variable coefficients are investigated numerically. Results show that the weak soliton interaction exists in PT-symmetric nonlinear coupler with periodically distributed dispersion and nonlinear parameters. There exists weak soliton interaction under different initial conditions, including two or three non-inverting input solitons with equal amplitude and three solitons with two inverting input solitons. Stability of the weak soliton interaction is discussed with finite initial perturbation. Results show that the main characteristics of weak soliton interaction can not be influenced by the finite initial perturbation.