They didn't support each other militarily. The Eastern Empire was generally stronger, so it allowed invading tribes to focus on the weak point in the West. Some historians would say that the Roman Empire stopped expanding and it needed that expansion in order to keep getting more land and more slaves that really drove its economy. One major factor probably was the Huns that caused this great migration in the fourth and fifth centuries that caused the Germanic tribes to cross the Rhine and cross the Danube and become either, or either settle as part of the Roman Empire or threaten the Roman Empire. Another theory, and all of these are probably contributors, is that as the Germanic tribes settled, they actually became more and more part of the Roman military. And some of them were officially part of the military. Some of them were mercenaries, soldiers for fortune, paid soldiers.