  We outline the prospects for performing pioneering radio weak gravitational
lensing analyses using observations from a potential forthcoming JVLA Sky
Survey program. A large-scale survey with the JVLA can offer interesting and
unique opportunities for performing weak lensing studies in the radio band, a
field which has until now been the preserve of optical telescopes. In
particular, the JVLA has the capacity for large, deep radio surveys with
relatively high angular resolution, which are the key characteristics required
for a successful weak lensing study. We highlight the potential advantages and
unique aspects of performing weak lensing in the radio band. In particular, the
inclusion of continuum polarisation information can greatly reduce noise in
weak lensing reconstructions and can also remove the effects of intrinsic
galaxy alignments, the key astrophysical systematic effect that limits weak
lensing at all wavelengths. We identify a VLASS "deep fields" program (total
area ~10-20 square degs), to be conducted at L-band and with high-resolution
(A-array configuration), as the optimal survey strategy from the point of view
of weak lensing science. Such a survey will build on the unique strengths of
the JVLA and will remain unsurpassed in terms of its combination of resolution
and sensitivity until the advent of the Square Kilometre Array. We identify the
best fields on the JVLA-accessible sky from the point of view of overlapping
with existing deep optical and near infra-red data which will provide crucial
redshift information and facilitate a host of additional compelling
multi-wavelength science.

Cosmology and Nongalactic Astrophysics