1) What sorts of factors influence the balance of power between the branches?
The system of checks and balances is an important part of the Constitution. With checks and balances, each of the three branches of government can limit the powers of the others. This way, no one branch becomes too powerful.
2) How has the balance of power between the branches shift?
This delicate balance of power is written into the US Constitution, but it's actually changed over time. None of the three branches looked the same in 1787 as they do now, but as long as they changed together, no branch became more powerful than the others, and the game continued.
I hope this helps