FWIW - compared to the U.S. President or the chief executives of other states, the Texas Governor occupies a "weak" office.
The main source of the relative weakness of the Texas Governor can be found in the historical conditions surrounding the
Texas Constitution of 1876. Mindful of the experience of Reconstruction - the period after the Civil War when Republican governors wielded extensive executive powers and were resisted by conservative elites in the state - the authors of the new constitution sought to rein in future governors. They did so by dispersing power that might otherwise be lodged in the chief executive's hands among a vast array of independently elected officials. Broad powers over the legal system, state budget and finances, education, transportation, agriculture, public utilities, and land development are delegated to officials who need not share the policies nor even be of the same political party as the governor.
The dispersal of power among different officials creates what is often called the plural executive. Unlike the federal system, where the cabinet secretaries and the other top executive officers serve at the pleasure of the President, the voters elect the corresponding officials in the Texas system, giving the Governor no direct authority over them.
As for the
10th Amendment, there's a good discussion of the complexity of its meaning over the years at
http://www.law.cornell.edu/anncon/html/amdt10_user.html
Richard's $.02