  (I) We observed eight Seyfert~2s and two X--ray--weak Seyfert~1/QSOs with the
ROSAT PSPC, and one Seyfert~2 with the ROSAT HRI. These targets were selected
from the Extended 12\um\ Galaxy Sample. (II) Both Seyfert~1/QSOs vary by
factors of 1.5---2. The photon indices steepen in the more luminous state,
consistent with the variability being mainly due to the softest X--rays, which
are confined to a size of less than a parsec. (III) Both the Seyfert~2s and
Seyfert~1/QSOs are best fit with a photon index of $\Gamma\sim3$, which is
steeper than the canonical value of $\Gamma\sim1.7$ measured for X--ray--strong
Seyferts by ROSAT and at higher energies. Several physical explanations are
suggested for the steeper slopes of X--ray--weak objects. (IV) We observed one
Seyfert~2, NGC~5005, with the ROSAT HRI, finding about 13\% of the soft X--rays
to come from an extended component. This and other observations suggest that
different components to the soft X--ray spectrum of some, if not all,
X--ray--weak Seyferts may come from spatially distinct regions.
