  We consider the (gauged) Weyl gravity action, quadratic in the scalar
curvature ($\tilde R$) and in the Weyl tensor ($\tilde C_{\mu\nu\rho\sigma}$)
of the Weyl conformal geometry. In the absence of matter fields, this action
has spontaneous breaking in which the Weyl gauge field $\omega_\mu$ becomes
massive (mass $m_\omega\sim$ Planck scale) after "eating" the dilaton in the
$\tilde R^2$ term, in a Stueckelberg mechanism. As a result, one recovers the
Einstein-Hilbert action with a positive cosmological constant and the Proca
action for the massive Weyl gauge field $\omega_\mu$. Below $m_\omega$ this
field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert
action is then just a "low-energy" limit of Weyl quadratic gravity which thus
avoids its previous, long-held criticisms. In the presence of matter scalar
field $\phi_1$ (Higgs-like), with couplings allowed by Weyl gauge symmetry,
after its spontaneous breaking one obtains in addition, at low scales, a Higgs
potential with spontaneous electroweak symmetry breaking. This is induced by
the non-minimal coupling $\xi_1\phi_1^2 \tilde R$ to Weyl geometry, with Higgs
mass $\propto\xi_1/\xi_0$ ($\xi_0$ is the coefficient of the $\tilde R^2$
term). In realistic models $\xi_1$ must be classically tuned $\xi_1\ll \xi_0$.
We comment on the quantum stability of this value.
