  We present a weak lensing analysis for galaxy clusters from the APEX-SZ
survey. For $39$ massive galaxy clusters that were observed via the
Sunyaev-Zel\textquotesingle dovich effect (SZE) with the APEX telescope, we
analyse deep optical imaging data from<EMAIL_ADDRESS>and
Suprime-Cam(@SUBARU) in three bands. The masses obtained in this study,
including an X-ray selected subsample of 27 clusters, are optimised for and
used in studies constraining the mass to observable scaling relations at fixed
cosmology. A novel focus of our weak lensing analysis is the multi-colour
background selection to suppress effects of cosmic variance on the redshift
distribution of source galaxies. We investigate the effects of cluster member
contamination through galaxy density, shear profile, and recovered
concentrations. We quantify the impact of variance in source redshift
distribution on the mass estimate by studying nine sub-fields of the COSMOS
survey for different cluster redshift and manitude limits. We measure a
standard deviation of $\sim 6$\% on the mean angular diameter distance ratio
for a cluster at $z\!=\!0.45$ and shallow imaging data of $R\!\approx\!23$ mag.
It falls to $\sim 1$\% for deep, $R=26$ mag, observations. This corresponds to
8.4\% and 1.4\% scatter in $M_{200}$. Our background selection reduces this
scatter by $20-40$\%, depending on cluster redshift and imaging depth. We
derived cluster masses with and without using a mass concentration relation and
find consistent results, and concentrations consistent with the used
mass-concentration relation.
