We study the particle spectrum and the unitarity of the generic n-dimensional Weyl-invariant quadratic curvature gravity theories around their (anti-)de Sitter and flat vacua. Weyl symmetry is spontaneously broken in (anti-)de Sitter and radiatively broken at the loop level in flat space. Save the three-dimensional theory (which is the Weyl-invariant extension of the new massive gravity), the graviton remains massless and the unitarity requires that the only viable Weyl-invariant quadratic theory is the Weyl-invariant extension of the Einstein-Gauss-Bonnet theory. The Weyl gauge field, on the other hand, becomes massive. The symmetry breaking scale fixes all the dimensionful parameters in the theory.