We numerically investigate force structures in the packing of fine cohesive particles using the discrete element method. By changing the particle size and therefore the van der Waals force, the effect of cohesion on the normal contact force and the total normal force, which is the sum of the normal contact forces and the van der Waals forces, is analyzed. It is shown that, with decreasing particle size, the normal contact forces become more uniform and have a narrower and more symmetric distribution, while the distributions of the total normal forces widen. Spatial correlation between the interparticle forces exists for the packing of coarse noncohesive particles. As the particle size decreases, this correlation becomes weaker for the contact forces but stronger for the total normal forces. A comparison between the effective weight of particles and the internal force structure suggests that there are differences between the particle-particle and particle-wall forces. The bimodal distribution of the effective weight indicates that there may exist two phases in the packings when cohesion is present, governed by the compressive and tensile stresses.