  The weak $(1,1)$ boundedness of the Littlewood--Paley--Stein square function
for the Dunkl heat flow is proved via estimates on the Dunkl heat kernel and
the Caldr\'{o}n--Zygmund decomposition, which is the continuity of the recently
joint work [arXiv:2003.11843] where the $|G|$-free (i.e., independent of the
order of $G$) and dimension-free $L^p$ boundedness of the same square function
is studied.
