Confined liquid films with a thickness in the range of a few molecular diameters exhibit different mechanical properties than in the bulk. With the technique of a 2-dimensional (2D) imaging surface forces apparatus (SFA) we investigated in detail the layer by layer thinning of a thin liquid film confined between two atomically smooth surfaces upon pressing them towards each other with increasing load. The dynamics of a series of subsequent squeeze-out processes of individual layers were analyzed. Using a simple hydrodynamic model, we extracted the thickness-dependence of the viscosity. For the system investigated here—the model lubricant Octamethylcyclotetrasiloxane (OMCTS) confined between ultraclean, recleaved mica surfaces—we found that the viscosity increased by a factor of 10 with decreasing the film thickness from 6 to 2 layers. We decomposed the friction into two components, one describing the sliding of liquid layers on top of the substrates, and the other describing liquid-on-liquid sliding. The latter contribution was found to agree closely with expectations based on the bulk viscosity, whereas the former was approximately 35 times higher for the present system.