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ABSTRACT Expanding from previous work, we present weak-lensing (WL) measurements for a total sample of 30 distant (zmedian = 0.93) massive galaxy clusters from the South Pole Telescope Sunyaev–Zel’dovich (SPT-SZ) Survey, measuring galaxy shapes in Hubble Space Telescope (HST) Advanced Camera for Surveys images. We remove cluster members and preferentially select z ≳ 1.4 background galaxies via V − I colour, employing deep photometry from VLT/FORS2 and Gemini-South/GMOS. We apply revised calibrations for the WL shape measurements and the source redshift distribution to estimate the cluster masses. In combination with earlier Magellan/Megacam results for lower-redshifts clusters, we infer refined constraints on the scaling relation between the SZ detection significance and the cluster mass, in particular regarding its redshift evolution. The mass scale inferred from the WL data is lower by a factor $0.76^{+0.10}_{-0.14}$ (at our pivot redshift z = 0.6) compared to what would be needed to reconcile a flat Planck νΛCDM cosmology (in which the sum of the neutrino masses is a free parameter) with the observed SPT-SZ cluster counts. In order to sensitively test the level of (dis-)agreement between SPT clusters and Planck, further expanded WL follow-up samples are needed.