How heavy should a Chinese chef's knife be? What weight should a Chinese chef's knife be and for what purpose?


All around, i.e. one knife for most cooking
Slicing
Chopping vegetables
Meat without bones
Chicken or fish with bones


Chinese chef's knife is left-most in the picture below.
A chinese style chef's knife, also known as the cai dow, or vegetable cleaver(trial subscription required, but an excellent article), is superficially similar to a western cleaver. The cleaver is typically a very robust blade, thick and weighty, meant for separating meat at the joint, splitting ribs and chops, and other tasks that require a lot of weight and a stiff blade.

The chinese chef's knife will be much thinner and lighter, comparable to a western chef's knife or Japanese nakiri. The broad face is for scooping up ingredients from the cutting board and controllability rather than mass and strength. From a brief blog entry from Kitchn on the knife -


  In her book Shark’s Fin and Sichuan Pepper: A Sweet-Sour Memoir of
  Eating in China, Fuchsia Dunlop explains, “The Chinese cleaver is not
  a butcher’s knife...The everyday cleaver, the cai dao or vegetable
  knife, is unexpectedly light and dexterous, as suitable for slicing a
  small shallot as a great hunk of meat, and used by everyone from the
  most macho chef to the frailest old lady.”