We present a maximum-likelihood weak-lensing analysis of the mass distribution in optically selected spectroscopic Galaxy Groups (G3Cv5) in the Galaxy And Mass Assembly (GAMA) survey, using background Sloan Digital Sky Survey (SDSS) photometric galaxies. The scaling of halo mass, Mh, with various group observables is investigated. Our main results are as follows. (1) The measured relations of halo mass with group luminosity, virial volume and central galaxy stellar mass, M*, agree very well with predictions from mock group catalogues constructed from a GALFORM semi-analytical galaxy formation model implemented in the Millennium ΛCDM N-body simulation. (2) The measured relations of halo mass with velocity dispersion and projected half-abundance radius show weak tension with mock predictions, hinting at problems in the mock galaxy dynamics and their small-scale distribution. (3) The median Mh|M* measured from weak lensing depends more sensitively on the lognormal dispersion in M* at fixed Mh than it does on the median M*|Mh. Our measurements suggest an intrinsic dispersion of σlog(M*)∼ 0.15. (4) Comparing our mass estimates with those in the catalogue, we find that the G3Cv5 mass can give biased results when used to select subsets of the group sample. Of the various new halo-mass estimators that we calibrate using our weak-lensing measurements, group luminosity is the best single-proxy estimator of group mass.