It's worth noting that most extinct dinosaurs were probably more similar to surviving ones (i.e., birds) than to mammals and reptiles when it comes to bones and respiratory systems, and, by extension, density.

That is to say, they probably could get that big because they were quite literally full of air.
Some of them (especially sauropods, but maybe also other big species like tyrannosaurs) probably had even more complex and efficient air sac systems than modern birds...