  Given a smooth, proper curve $C$ over a discretely valued field $k$, we equip
the $k$-vector space $H^{0}(C,\omega_{C/k})$ with a canonical discrete
valuation $v_{\mathrm{can}}$ which measures how canonical forms degenerate on
regular integral models of $C$. More precisely, $v_{\mathrm{can}}$ maps a
canonical form to the minimal value of its associated weight function, as
introduced by Musta\c{t}\u{a}--Nicaise. Our main result states that
$v_{\mathrm{can}}$ computes Edixhoven's jumps of the Jacobian of $C$ when
evaluated in an orthogonal basis. As a byproduct, we deduce a short proof for
the rationality of the jumps of Jacobians. We also show how $v_{\mathrm{can}}$
and the jumps can be computed efficiently for the class of $\Delta_v$-regular
curves introduced by Dokchitser.
