  It has been shown that the thin brane model in a five-dimensional Weyl
gravity can deal with the wrong-signed Friedmann-like equation in the
Randall--Sundrum-1 (RS1) model. In the Weyl brane model, there are also two
branes with opposite brane tensions, but the four-dimensional graviton (the
gravity zero mode) is localized near the negative tension brane, while our
four-dimensional universe is localized on the positive tension brane. In this
paper, we consider the mass spectra of various bulk matter fields (i.e.,
scalar, vector, and fermion fields) on the Weyl brane. It is shown that the
zero modes of those matter fields can be localized on the positive tension
brane under some conditions. The mass spectra of the bulk matter fields are
equidistant for the higher excited states, and relatively sparse for the lower
excited states. The size of the extra dimension determines the gap of the mass
spectra. We also consider the correction to the Newtonian potential in this
model and it is proportional to $1/r^{3}$.
