  We give a detailed analysis of the particle spectrum and the perturbative
unitarity of the recently introduced Weyl-invariant version of the new massive
gravity in 2+1 dimensions. By computing the action up to second order in the
fluctuations of the metric, the gauge and the scalar fields around the anti-de
Sitter (AdS) and flat vacua, we find that the theory describes unitary (tachyon
and ghost-free) massive spin-2, massive (or massless) spin-1 and massless
spin-0 excitations for certain ranges of the dimensionless parameters. The
theory is not unitary in de Sitter space. Scale invariance is either broken
spontaneously (in AdS background) or radiatively (in flat background) and hence
the masses of the particles are generated either spontaneously or at the second
loop order.
