We present weak lensing results for 12 distant clusters determined from images obtained with the refurbished HST. We detect the signature of gravitational lensing in 11 of the 12 clusters; the clusters span nearly an order of magnitude in lensing strength. The sample thus provides an excellent database for correlating direct mass estimates from lensing with indirect ones which rely on baryonic tracers. We examine the correlation between the cluster X-ray luminosities and the mean gravitational shear strengths and develop a model which predicts the relationship expected from the properties of local clusters. After allowing for various observational effects, we find that the predicted correlation is a reasonable match to the available data, indicating that there has been little evolution in the X-ray luminosity-central mass relationship between z=0.4 and now. We discuss the implications of this result in the context of the evolution of the X-ray luminosity function found by earlier workers. The comparison between shear amplitudes and velocity dispersions, estimated from a modest sample of members, reveals a discrepancy in the sense that these velocity dispersions are typically over-estimated by factors of ~50%. This supports earlier suggestions that high dispersions measured for distant clusters may be seriously affected by both unidentified substructure and outliers. Combining our lensing masses with morphologically-based luminosity estimates, we determine mass/light ratios in solar units of M/L_V=180+/-160 h for the entire population and 620+/-250 h for the spheroidal galaxies where the evolutionary effects can be best treated. We argue that this provides an upper bound to the local cluster M/L corresponding to Omega~0.4. Comment: 32 pages, Latex, 11 figures, accepted for publication in ApJ