  In this paper we investigate the moduli space of parabolic Higgs bundles over
a punctured Riemann surface with varying weights at the punctures. We show that
the harmonic metric depends analytically on the weights and the stable Higgs
bundle. This gives a Higgs bundle generalisation of a theorem of McOwen on the
existence of hyperbolic cone metrics on a punctured surface within a given
conformal class, and a generalisation of a theorem of Judge on the analytic
parametrisation of these metrics.
