The writers of the Constitution were very conscious of the need for a strong federal government, having seen the failure of the Articles of Confederation to satisfactorily support the new country. At the same time, however, the writers understood the importance of maintaining as much governmental authority as possible as close to the general population as possible.
Specific potential problems were addressed at several places in the Constitution. Article I Section 8 assigns authority to the national legislative body to handle many functions that had been left to individudal states, an arrangement that had proven unsatisfactory. Article I Section 10 forbids states from undertaking certain actions independent of the entire country.
Article IV establishes a common standing for all the states. No state has any particular advantages or restrictions within the union that was being created.
Article VI specifically spells out the supremacy of the United States national government's power over that of the individual states.
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land;...The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution;
This was the reassurance that the difficulties of the Articles of Confederation would not recur.