States’ Rights, sovereignty on state issues and an autonomy of the States on certain issues is a paramount foundational part of what the Constitution is all about, and such thinking is codified by the Tenth Amendment which indicates that if a power is not granted to the federal government by the Constitution, nor prohibited to the States, the power belongs to the States.
The Articles of Confederation had a great influence on the Constitution and the desire by the Founding Fathers to keep State identity and localism in place, but the Founding Fathers also realized that the Articles of Confederation were too weak in other arenas. For fear of a central government becoming too powerful, they made it not powerful enough. The Constitution, therefore, was all about seeking balance through a proper distribution of powers—strengthening the authorities of the central government on particular issues while keeping it limited on issues that needed to remain with the States.
In short, while the federal government was granted only limited powers, the authorities it was granted were to be carried out in a strong way. The Founding Fathers realized that for a central government they needed a lion, but the system was more like a lamb under the Articles of Confederation. But, a ferocious lion is capable of being a vicious animal against its handlers if allowed to run rampant domestically, so it was put in the cage of the Constitution to keep it under control when it came to We the People. That does not mean that the ferocious potential of the federal government was eliminated. The creature we call the federal government was allowed to keep its teeth and claws on purpose so that when it needed to be unleashed on certain issues it had the strength and capabilities to do so.
The Constitution is designed around a concept of “granted” powers. The original list of granted authorities are listed in Article I, Section 8. Other powers appear in other parts of the Constitution. According to Federalist Paper #45 by James Madison, those powers revolve mostly around external issues and disputes between the States. Sometimes, those issues also reach inward, which is when the federal government is authorized to operate domestically, as well.