This is essentially a cross-post from H2VP (with some additions)
One thing I have been asked with some regularity is whether or not a somewhat denser Mesozoic atmosphere, particularly in the Cretaceous (compared to the modern one), could explain the giant size of Late Cretaceous pterosaurs or large dinosaurs. In short, the answer is: probably not.
There is a reasonably good body of information regarding atmospheric composition during the Mesozoic. During the Cretaceous, both oxygen and carbon dioxide levels rose slightly, and the total atmospheric density would have been slightly greater as a result - but the difference would have been relatively mild for large vertebrates.
There are three reasons why changes in atmospheric conditions have greater impacts on insects than vertebrate flyers. First, the tracheal system that insects use for respiration is highly sensitive to oxygen partial pressure. Second, since insects are typically small, they are often highly reliant on unsteady aerodynamics, which are much more sensitive to air density than steady dynamics. Finally, insects are almost purely aerobic flyers, while many vertebrates can utilize some degree of anaerobic power (in large flying vertebrates, anaerobic power dominates). Using anaerobic flight muscle provides a very large burst of power, without using oxygen, after which the muscle quickly fatigues. Large vertebrates can therefore flap for short bursts, followed by periods of gliding, even when oxygen levels are low. This option is typically unavailable to insects.