  Large area surveys have detected significant samples of galaxy clusters that
can be used to constrain cosmological parameters, provided that the masses of
the clusters are measured robustly. To improve the calibration of cluster
masses using weak gravitational lensing we present new results for 48 clusters
at $0.05<z<0.15$, observed as part of the Multi Epoch Nearby Cluster Survey
(MENeaCS), and reevaluate the mass estimates for 52 clusters from the Canadian
Cluster Comparison Project (CCCP). Updated high-fidelity photometric redshift
catalogues of reference deep fields are used in combination with advances in
shape measurements and state-of-the-art cluster simulations, yielding an
average systematic uncertainty in the lensing signal below 5%, similar to the
statistical uncertainty for our cluster sample. We derive a scaling relation
with Planck measurements for the full sample and find a bias in the Planck
masses of $1-b=0.84 \pm 0.04$. We find no statistically significant trend of
the mass bias with redshift or cluster mass, but find that different selections
could change the bias by up to 1.5$\sigma$. We find a gas fraction of $0.139
\pm 0.014$ for 8 relaxed clusters in our sample, which can also be used to
infer cosmological parameters.
