We investigate the intermolecular-interaction and damping (among exciton states) effects an the polarizabilities (alpha) for molecular aggregates with different sizes of planar dendritic, i.e., Bethe-lattice (or Cayley-tree), structures by elucidating the spatial contribution of one-exciton generation to alpha. The molecular aggregate is treated in the one-exciton model, including the dipole-dipole interaction. The off-resonant or of the molecular aggregate is calculated by the numerical Liouville approach, including the damping effects. The signs of the contribution of intermolecular-interaction (positive) and damping (negative) effects to alpha are found to be opposite with each other. The magnitude of these effects on or indicates a nonlinear enhancement as the number of monomers increases. These effects on alpha for the fractal-structured dendritic aggregates are also found to provide distinct spatial contributions for different generations of the dendritic structure in contrast to the case of a non-fractal-structured dendritic aggregate.