The sedimentation equilibrium of a colloidal suspension modeled as a collection of adhesive hard-sphere particles confined in a planar slit pore is studied by using a density functional approach with a newly developed approximation in which the repulsive part of the adhesive hard-sphere interaction potential is treated within weighted density functional theory while the attractive part is evaluated by a third-order perturbative approach. The calculated density profiles obtained from this approach for the adhesive hard-sphere fluid confined in a slit pore in the absence of gravitational field is in excellent agreement with the available computer simulation results for varying pore sizes and stickiness parameters of the potential. The same approach applied to the study of the effect of gravitational field on the equilibrium structure of the system predicts density profiles exhibiting strong oscillation at the bottom of the pore with a decreasing tail approaching the upper wall. The interplay between the packing effect due to confinement by the walls, gravitational field, and attractive forces among the particles determines the structure of the density profiles. The effect of all these parameters on the distribution of the colloidal particles in the confined environment is investigated.