Context. Viscous dissipation is expected to play a significant part in energy release in solar flares, yet the role of viscosity in a weakly resistive plasma of the solar corona remains unclear. Aims. We attempt to clarify the role of viscous effects in magnetic reconnection by performing simulations of reconnection in planar periodic geometry in an incompressible viscous resistive plasma. Methods. We consider magnetic reconnection, driven by large-scale vortical flows. We use both the classical shear viscosity and the Braginskii form for the ion parallel viscosity in a magnetised plasma. We determine the scalings of the current sheet parameters and the global rates of resistive and viscous dissipation. We use steady-state exact solutions and scaling arguments to interpret the numerical results. Results. We show that, regardless of the form of viscosity, the resistive non-viscous analytical solutions for flux pile-up merging provide a very good approximation of the numerical results in the reconnecting current sheet. We find no evidence for a visco-resistive scale. Numerical results for a highly sheared magnetic field, however, appear to deviate from the analytical predictions in the case of the Braginskii viscosity.