Depends on the dinosaur. Some such as compsagnathus were only about the size of chicken and maybe weighing a little more that one to the enourmous seismosaurus or ultrasaurus both weighing from 130 tons to almost 150 tons!
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Last I checked, nothing confirmed what Barney would have supposedly weighed. (playing as the character, not the actual weight combined by the person in the costume, and the costume itself)