The reactions induced by the weakly bound 6Li projectile interacting with the intermediate mass target 59Co were investigated. Light charged particles singles and $alpha$-$d$ coincidence measurements were performed at the near barrier energies E_lab = 17.4, 21.5, 25.5 and 29.6 MeV. The main contributions of the different competing mechanisms are discussed. A statistical model analysis, Continuum-Discretized Coupled-Channels calculations and two-body kinematics were used as tools to provide information to disentangle the main components of these mechanisms. A significant contribution of the direct breakup was observed through the difference between the experimental sequential breakup cross section and the CDCC prediction for the non-capture breakup cross section.