Little Barrier Island giant weta or Wetapunga (Deinacrida heteracantha) from New Zealand is regarded to be the world's biggest insect, more certainly to say the heaviest. The scientific name of the genus is Deinacrida, which in means "Terrible grasshopper" in the Greek language. There is documented specimen of 71gr, which is heavier than sparrow or mouse. As well there are more insects pretending for the title largest, mostly of them beetles, but there is not documented heavier specimen as far as I know.
Update: There are actually bigger insects if we consider also the larvae of some beetles. However the Wetapunga is still the biggest adult (imago) form.
Update N2: Also, apparently Wetapunga means "God of ugly things" in Maori (for the authenticity of which I can't guarantee, but I don't see reason why the guy from the comment section is going to lie)