When people look of non-avian dinosaur they're thinking of extrapolating a cow up to that size. Mammals are much much denser than birds are, because a lot of the skeletons of sauropods (the big, long-necked ones—Apatosaurus, Brachiosaurus and the like) and theropod dinosaurs are just air. Theropods don't have solid bones like we do; they have hollow bones. Sauropods don't, but they have tremendous air sacs that fill up a lot of their bodies. And thus they weigh way less than a mammal scaled up to that size.
As quoted in "How Dinosaurs Loved: An Interview with Dr. Mark Norell on Dino Relations", Vice (March 20, 2012)