The sedimentation equilibrium of adhesive spheres mimicking a system of interacting spherical colloidal particles in suspensions in planar pores is considered The density profiles of the adhesive fluid in a gravitational field, and its distribution between the pores and the homogeneous phase are studied on the basis of the solution to the hypernetted chain/Ornstein-Zernike equation, obtained by using the analytic results for the direct correlation function of the bulk fluid. In a few cases, the Percus-Yevick closure is also used. In the hard sphere limit, both integral equation approaches are compared with the results of a grand canonical ensemble Monte Carlo simulation. This comparison shows, in particular in narrow pores, that the hypernetted chain approximation provides a better estimate for the structure of the hard sphere fluid in the pore, as well as for its partitioning between the bulk and the confined system. The calculated density profiles consist of an oscillatory part near the lower wall revealing layering, and a monotonically decreasing tail approaching the upper wall, their shapes being very sensitive to the strength of interparticle attraction, the strength of the gravitational field, and the degree of confinement. Increasing interparticle adhesive attraction together with gravity results in the particles occupying the region of lower altitudes in the gap and being partly squeezed out from the pore.