Why did the Roman Empire collapse?

My understanding is that when Caesar crossed the Rubicon it was the end of the Roman Republic and the beginning of the Roman Empire.

I saw a documentary that thought lead in the water pipes might have been a factor. Not the only reason.

Rome got too big and top-heavy for its economy to sustain. It was a huge, corrupt bureaucratic military machine. It was able to sustain itself on the plunder obtained through conquest and plunder of new lands, but after the empire hit its geographical limits it began to decline. It was based on the slave mode of production, which worked well so long as there was a constant supply of new slaves, but the supply of slaves came mostly from war. Once Rome's expansion came to a halt, the supply of slaves declined. There was still an international slave trade, and slaves could of course reproduce and give birth to new slaves, but this wasn't enough to meet the demands of Rome's massive economy. The slave mode of production had hit its limits and gradually began to decline, becoming less and less profitable over time. Roman slavery had also greatly harmed the agriculture of its Italian heartland (the original foundation of Rome's power), as the smallholding peasants were ruined because they couldn't compete with the big slave estates which gobbled up their land, and production had shifted more and more from staples to cash crops that benefited only the big landowners. Rome became dependent on its overseas territories (particularly Egypt) to feed itself. Italy's economy could no longer sustain the empire. The empire was massive, and required a huge military machine to maintain its borders. This placed an onerous burden on the Roman economy, which gradually weakened due to the limits of expansion, the decline of slavery and the ruin of Italian agriculture. Without the plunder to be gained from expansion, the empire had to increase the tax burden on its population higher and higher to maintain itself and sustain both the huge military machine and the lavish lifestyle the rich had become accustomed to at the empire’s height. This further crippled the peasantry, not just in Italy but all over the empire.

Meanwhile the so-called "barbarians" were becoming more sophisticated economically and militarily, developing more powerful states and tribal organizations that the Romans had a harder time contending with. Not that this relationship was always antagonistic; the "barbarians" worked for the Romans as often as they worked against them, and over time, as the Roman military faced severe manpower problems due to the economic decline, the Romans became more and more dependent on the "barbarians" themselves to defend the borders. Which they were often perfectly happy to do in exchange for being given land within the empire, but the problem was the chauvinistic Romans treated them like garbage (making them prone to rebellion), not a very wise thing to do to the people you depend on for military defense.

The split of the empire into western and eastern halves greatly exacerbated all of these problems, because the west was nowhere near as rich as the east, so without the wealth of the east, the west could not sustain itself. Cities and towns declined, no longer economically viable. Cities in antiquity were essentially parasitic, not so much centers of production as they are today, and with the empire’s economic decline, it was no longer possible to sustain the cities. The city of Rome itself was reduced over the years from a population of about a million to a few tens of thousands. The western empire eventually fell, crushed under the weight of its own contradictions.

The eastern empire went on for another thousand years, though in a more and more truncated form as time went on. It suffered from some of the same problems, but it was richer and more developed than the west and had shorter and more defensible frontiers, so it was able to sustain itself for longer and withstand the transition to a new medieval economy. But it still had some of the same problems, in addition to new ones like issues of managing religious strife as Christianity split into more and more sects. Part of the reason why the new Muslim Caliphate was able to conquer the Levant and North Africa so easily was because the local population largely welcomed the end of Roman rule and its system of rapacious exploitation and onerous taxation as well as religious persecution. Even with the jizya tax on non-Muslims, the economic burden on the population was greatly reduced, and Christian sects that weren’t aligned with the official doctrine of Constantinople found that they had greater freedom in the Dar al-Islam. The Byzantine Empire was a sort of fossil of the old Roman political and military system, and although it did manage to adapt itself to some extent to the new world, it was plagued by chronic instability and was never able to regain its old power and relevance, and it was gradually eclipsed and overwhelmed by the new and more dynamic and stable feudal polities of Europe and particularly the Middle East.

From what I read, it came far too corrupt from within, and became too big to manage over time. Different factions within the empire bickered with each other too much, and then didn't notice until it was too late when the Visigoths invaded.

long supply lines and lack of central control.