  We present a Hubble Space Telescope (HST) weak gravitational lensing study of
nine distant and massive galaxy clusters with redshifts $1.0 \lesssim z
\lesssim 1.7$ ($z_\mathrm{median} = 1.4$) and Sunyaev Zel'dovich (SZ) detection
significance $\xi > 6.0$ from the South Pole Telescope Sunyaev Zel'dovich
(SPT-SZ) survey. We measured weak lensing galaxy shapes in HST/ACS F606W and
F814W images and used additional observations from HST/WFC3 in F110W and
VLT/FORS2 in $U_\mathrm{HIGH}$ to preferentially select background galaxies at
$z\gtrsim 1.8$, achieving a high purity. We combined recent redshift estimates
from the CANDELS/3D-HST and HUDF fields to infer an improved estimate of the
source redshift distribution. We measured weak lensing masses by fitting the
tangential reduced shear profiles with spherical Navarro-Frenk-White (NFW)
models. We obtained the largest lensing mass in our sample for the cluster
SPT-CLJ2040$-$4451, thereby confirming earlier results that suggest a high
lensing mass of this cluster compared to X-ray and SZ mass measurements.
Combining our weak lensing mass constraints with results obtained by previous
studies for lower redshift clusters, we extended the calibration of the scaling
relation between the unbiased SZ detection significance $\zeta$ and the cluster
mass for the SPT-SZ survey out to higher redshifts. We found that the mass
scale inferred from our highest redshift bin ($1.2 < z < 1.7$) is consistent
with an extrapolation of constraints derived from lower redshifts, albeit with
large statistical uncertainties. Thus, our results show a similar tendency as
found in previous studies, where the cluster mass scale derived from the weak
lensing data is lower than the mass scale expected in a Planck $\nu\Lambda$CDM
(i.e. $\nu$ $\Lambda$ Cold Dark Matter) cosmology given the SPT-SZ cluster
number counts.
