I too am researching my family in Graz - the Markl/Markel family as well as Weiss. My great great great grandmother was Theresia Weiss. She married Franz Markl a master tailor in Graz in 1807, was born around 1789(I don't know exactly where) and died in 1827 in Graz. Her father was listed as a landschaftlichen kannoniers which literally means landscape gunner - so perhaps was a hunter?
Maybe this helps.