First, we have to determine what weak and corrupt rulers mean. It means that those governors, despite the way they rose to power (monarchy, democracy, dictatorship) are not able to manage their plans or they deliberately decided to not pursue them. In this case following, a corrupt path of personal enrichment. Now let's investigate how they can affect the government.
Knowing all the power that is given to some statesmen, such as power over the Senate, over the parliament, the power to manipulate a previous constitution and to create a coalition to defend their own personal plan of power, it can deeply affect the government. It is well known, from past experiences in our history, the bad results of weak rulers, leading their countries to complete social turmoil, economic stagnation and political mess. The same with corrupt rulers that led the country in an unsustainable political, social and economic scenario.
But the vast damage can be seen in the economic sphere. By attacking the very basic human need of exchange goods and services, weak and corrupt rulers led their communities to a high decline in the standards of leaving, and in an ultimate analysis, to generalized starvation.