  We present XMM-Newton imaging spectroscopy of ten weak emission-line quasars
(WLQs) at $0.928\leq z \leq 3.767$, six of which are radio quiet and four which
are radio intermediate. The new X-ray data enabled us to measure the power-law
photon index, at rest-frame energies $>2$ keV, in each source with relatively
high accuracy. These measurements allowed us to confirm previous reports that
WLQs have steeper X-ray spectra, suggesting higher accretion rates with respect
to 'typical' quasars. A comparison between the photon indices of our
radio-quiet WLQs and those of a control sample of 85 sources shows that the
first are significantly higher, at the >~$3\sigma$ level. Collectively, the
four radio-intermediate WLQs have lower photon indices with respect to the six
radio-quiet WLQs, as may be expected if the spectra of the first group are
contaminated by X-ray emission from a jet. Therefore, in the absence of
significant jet emission along our line of sight, these results are in
agreement with the idea that WLQs constitute the extreme high end of the
accretion rate distribution in quasars. We detect soft excess emission in our
lowest-redshift radio-quiet WLQ, in agreement with previous findings suggesting
that the prominence of this feature is associated with a high accretion rate.
We have not detected signatures of Compton reflection, Fe K$\alpha$ lines, or
strong variability between two X-ray epochs in any of our WLQs, which can be
attributed to their relatively high luminosity.
