  We perform a measurement of the mass--richness relation of the redMaPPer
galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky
Survey. We have carefully characterized a broad range of systematic
uncertainties, including shear calibration errors, photo-$z$ biases, dilution
by member galaxies, source obscuration, magnification bias, incorrect
assumptions about cluster mass profiles, cluster centering, halo triaxiality,
and projection effects. We also compare measurements of the lensing signal from
two independently-produced shear and photometric redshift catalogues to
characterize systematic errors in the lensing signal itself. Using a sample of
5,570 clusters from $0.1\le z\le 0.33$, the normalization of our power-law mass
vs.\ $\lambda$ relation is $\log_{10}[M_{200m}/h^{-1}\ M_{\odot}]$ = $14.344
\pm 0.021$ (statistical) $\pm 0.023$ (systematic) at a richness $\lambda=40$, a
7 per cent calibration uncertainty, with a power-law index of
$1.33^{+0.09}_{-0.10}$ ($1\sigma$). The detailed systematics characterization
in this work renders it the definitive weak lensing mass calibration for SDSS
redMaPPer clusters at this time.
