One factor that has led to the national government having significantly more power than the state governments has been the increasing complexity and interconnection of the American economy.
The Constitution gave Congress the exclusive right to regulate interstate commerce. Over time, this right has given the federal government more and more power over the states. When the Constitution was written, most economic activity took place within states and so the federal government had very little regulating to do. Nowadays, though, almost all economic activity involves interstate commerce. A hamburger that you buy at McDonald's for example, will have beef from one state, tomatoes from another, a bun made from wheat from yet another state. All of that has been transported across state lines. This means that it is all regulated by the federal government.
As the American economy has grown bigger and more interconnected, the federal government's right to regulate interstate commerce has greatly increased its power relative to that of the states.