Exclusive breakup measurements have been performed for the 6 Li + p system in inverse kinematics at 6 Li incident energies of 25 and 29 MeV. The results are considered in the Continuum Discretized Coupled-Channels framework, together with elastic scattering data at 16, 20, 25, and 29 MeV, obtained simultaneously in the same experiment and reported previously. Good agreement between data and theory is observed, interpreted as evidence for strong coupling to the continuum. The direct and sequential (via the 6 Li 3 1 + resonance) breakup cross sections are found to be equally large at the higher incident energies but the dominant effect on the elastic scattering is due to coupling to the sequential breakup. This effect remains dominant even at the lowest energy of 16 MeV, despite the negligible cross section for excitation of the resonance at this low incident energy.