  We determine the affine Weyl symmetries of some two-dimensional birational
maps known as QRT roots arising from Kahan--Hirota--Kimura discretisation of
two different reduced Nahm systems. The main finding is that the symmetry types
of these discrete systems are subgroups of the Weyl groups for Sakai's discrete
Painlev\'e equations to which the QRT maps are the autonomous limits.
