There are several examples where the largest animals were killed off preferentially due to a major ecological shift:
- The KT extinction event
- The Holocene extinction, as well as the major megafauna humans killed off
The common ancestor of modern mammals is thought to be "shrew-like" in size, and it differentiated into most of the large animal species in the world today. I imagine that a similar statement can be made for dinosaurs. In general it seems that a major extinction event is likely to be best weathered by smaller creatures which can later, over time, increase in size to fill the niche that larger animals, and evolution dictates it will be profitable to do so.
Does this limit large animals to only the branches of the tree of life? Any given set of (Multicellular) species obviously share a common ancestor that is much smaller than them. Is it possible for many species to share a common ancestor that is considerably larger than any of them?