What factors contribute to the strength or weakness, constitutionally, of a state's governor?

Answer 1

The only factors for each state that would influence the powers of that state's governor would be the governmental structure and powers given to that governor per his or her state constitution.

I am saying that each state's constitution lays out the powers of its governor much like the national constitution lays out the powers of the Executive Branch and Congress on the federal level.

Answer 2

The governor is given the power to administer the state by the constitution like a little President but his acts must be within the delegated powers as intended by Congress.