Continuum Discretized Coupled-Channel (CDCC) model calculations of total, complete and incomplete fusion cross sections for reactions of the weakly bound 6Li with 144,154Sm targets at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li→α+d, short-range absorption potentials are considered for the interactions between the ground state of the projectile 6Li and α-d fragments with the target. In order to separately calculate complete and incomplete fusion and to reduce double-counting, the corresponding absorption potentials are chosen to be of different range. Couplings to low-lying excited states 2+, 3− of 144Sm and 2+, 4+ of 154Sm are included. So, the effect on total fusion from the excited states of the target is investigated. Similarly, the effect on fusion due to couplings to resonance breakup states of 6Li, namely, l=2, Jπ=3+,2+,1+ is also calculated. The latter effect is determined by using two approaches, (a) by considering only resonance state couplings and (b) by omitting these states from the full discretized energy space. Among other things, it is found that both resonance and non-resonance continuum breakup couplings produce fusion suppression at all the energies considered.