A new weighted density functional theory for inhomogeneous fluids is developed by combining the functional Taylor expansion of the perturbative approach with the nonperturbative weighted density concept. In this approach, the functional Taylor expansion of the one-particle direct correation function (DCF) is truncated at second order and the effect of a subset of the higher order terms is taken into account by evaluating the third-order DCF at a suitable weighted density, determined by demanding the fourth order DCF to be reproduced from the proposed expansion in the homogeneous limit. The present approach uses as input the two-particle DCF of the corresponding uniform fluid along with an approximation to the three-particle DCF. The proposed theory is applied to hard sphere as well as Lennard-Jones fluids in confined geometries, and the calculated density profiles for both the systems are shown to be in very good overall agreement with the available simulation data.