Density functional theory has been used to investigate the behavior of the π electrons in bilayer graphene and graphite under compression along the c axis. We have studied both conventional Bernal (A-B) and A-A stackings of the graphene layers. In bilayer graphene, only about 0.5% of the π-electron density is squeezed through the sp2 network for a compression of 20%, regardless of the stacking order. However, this has a major effect, resulting in bilayer graphene being about six times softer than graphite along the c axis. Under compression along the c axis, the heavily deformed electron orbitals (mainly those of the π electrons) increase the interlayer interaction between the graphene layers as expected, but, surprisingly, to a similar extent for A-A and Bernal stackings. On the other hand, this compression shifts the in-plane phonon frequencies of A-A stacked graphene layers significantly and very differently from the Bernal stacked layers. We attribute these results to some sp2 electrons in A-A stacking escaping the graphene plane and filling lower charge-density regions when under compression, hence, resulting in a nonmonotonic change in the sp2-bond stiffness.