We report the masses of the lightest spin-0 and spin-2 glueballs obtained in an extensive lattice study of the continuum and infinite volume limits of Sp(Nc) gauge theories for Nc=2, 4, 6, 8. We also extrapolate the combined results toward the large-Nc limit. We compute the ratio of scalar and tensor masses, and observe evidence that this ratio is independent of Nc. Other lattice studies of Yang-Mills theories at the same space-time dimension provide a compatible ratio. We further compare these results to various analytical ones and discuss them in view of symmetry-based arguments related to the breaking of scale invariance in the underlying dynamics, showing that a constant ratio might emerge in a scenario in which the 0++ glueball is interpreted as a dilaton state.