Below-barrier no-capture breakup measurements of the weakly bound {sup 9}Be nucleus, incident on targets ranging in atomic number from 62 to 83, have been carried out using a large-area high-resolution back-angle detector array. It is shown that the three-body reconstructed reaction Q-value and relative energy of the breakup fragments together reveal the full dynamics of the breakup mechanism, identifying all physical processes that lead to the breakup of the projectile-like nucleus. Contrasting with the simple expectation of direct breakup into the most energetically favored clusters, the data show that breakup following n-transfer dominates the total breakup yield. Breakup from long-lived states in the projectile-like nucleus, which on the reaction time scale may be considered stable, has been isolated from the prompt breakup yield. It has been shown that the prompt breakup probability essentially depends on the surface separation of the interacting nuclei. The measured prompt breakup probability functions for each target have been used together with a classical trajectory model to predict the above-barrier suppression of complete fusion. The suppression factor, expressed as the fraction of incomplete fusion, is nearly independent of target charge.