From 395 AD onwards, the Roman empire seemed to have split into two. The people of rome may have not seen it as a split, but they were administered by a separate and independent imperial court. They were considered coequal courts dividing the governance for smoother functioning of the vast and ever expanding empire. This term Western Roman Empire and Eastern Roman Empire are only modern terminology trying to explain their situation.
Intermitently, the rule of the Western Roman empire shifted from being independent to being ruled by the same person as in the East. But either way, the West was not able to hold its own as it lost several regions along the way. These losses were due to political and religious factors that the rulers had difficulty controling. Possibility there was less stability in the rulership of the Western Roman empire and that may have been the cause of the West being weaker in many ways.
No, the Western Roman Empire was not weak from the start. It only lost its greatness and power when the Barbarians invaded them. The territory was divided and led by different policies. The west empire started losing its strength when the health of the people especially the soldiers declined. This allowed invaders to enter the empire easily.
It never bounced back to their old power losing financial, military, and political strength unlike the Eastern Empire survived and continued to be one of the most powerful empires ever recorded. Many leaders tried recovering the west empire but their efforts were futile as the west are more scattered in beliefs and their leaders were not as capable as their ancestors or the current leaders of the eastern empire.