How did weak government help lead to the fall of Rome?

Historians have always debated the exact cause for Rome's fall, but there is a general agreement that one of the leading factors in it's collapse was that it simply became too large to control from a central point. The empire split in half because the language and culture in the east and west were drastically different, and that weakened the poorer western part of the empire greatly. In addition to this, some historians think that members of Rome's upper class (particularly the emperors) may have ingested large amounts of lead in their drinking water. Pipes in the Roman Empire were constructed with lead, which would sometimes erode away into the water that people drank. This may have led to the emperors becoming mentally unstable (a prime example of their mental instability is the fact that one Roman emperor married a horse, and yes, this really did happen, this is not vandalism or a joke). A few historians also think that malaria may have played a role in the destruction of the Roman empire. Mosquitos carrying malaria lived around the rivers that cut paths through the city until a relatively short time ago, and may have helped to weaken the city. The historians who believe this point to documents that describe sickness and disease in the city not long before it's fall. I hope this helps you to better understand the fall of the Roman Empire.