  In this paper we discuss on the phenomenological viability of nonmetricity
theories of gravity which are based in the class of generalized Weyl spacetimes
-- denoted by $W_4$ -- where arbitrary nonmetricity is allowed. This class of
geometry includes the so called teleparallel spaces $Z_4$, which are the
geometric basement of the symmetric teleparallel theories (STTs). The guiding
principle in our discussion is Weyl gauge symmetry (WGS), which is a manifest
symmetry of $W_4$ spaces. Here we derive the master equation that drives the
gauge invariant variations of the length of vectors during parallel transport
in $W_4$. This is the mathematical basis of the second clock effect (SCE). We
are able to give qualitative and quantitative estimates for the SCE, as well as
for the perihelion shift, in the coincident gauge of $Z_4$ space. We conclude
that generalized Weyl spaces do not represent phenomenologically viable
descriptions of Nature due to the SCE and, also to their predictions for the
perihelion shift. All of the present results are based in the assumption of:
(i) a gauge invariant parallel transport law and (ii) a consistency hypothesis
which enables identifying hypothetical vectors and tensors defined in $W_4$,
with related physical vectors and tensors arising in the given gravitational
theory. Our discussion is mostly geometrical without relying on specific
theories of gravity, unless it is absolutely necessary.
