  We construct a class of static, axially symmetric solutions representing
razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in
Found. Phys. 29, 1303 (1999). The main differences between these solutions and
the corresponding general relativistic one are analyzed, focusing on the
behavior of physical observables (rotation curves of test particles, density
and pressure profiles). We consider the case in which test particles move on
Weyl geodesics. The same rotation curve can be obtained from many different
solutions of the Weyl-Dirac theory, although some of these solutions present
strong qualitative differences with respect to the usual general relativistic
model (such as the appearance a ring-like density profile). In particular, for
typical galactic parameters all rotation curves of the Weyl-Dirac model present
Keplerian fall-off. As a consequence, we conclude that a more thorough analysis
of the problem requires the determination of the gauge function $\beta$ on
galactic scales, as well as restrictions on the test-particle behavior under
the action of the additional fields introduced by this theory.
