  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 of
integral type and the Caldr\'{o}n--Zygmund decomposition, which is the
continuity of the recently work [arXiv:2003.11843] where the dimension-free
$L^p$ boundedness of the same square function is studied.
