The Federalist #62 explains that by having the state legislatures appoint U.S. Senators it would serve as a check on federal power by the state governments.
“It is recommended by the double advantage of favoring a select appointment, and of giving to the State governments such an agency in the formation of the federal government as must secure the authority of the former, and may form a convenient link between the two systems.” [emphasis added]
“Another advantage accruing from this ingredient in the constitution of the Senate is, the additional impediment it must prove against improper acts of legislation. No law or resolution can now be passed without the concurrence, first, of a majority of the people, and then, of a majority of the States.” [emphasis added]
This clearly provides an additional check on federal usurpation of powers reserved to the state governments under the Constitution. Because all laws have to pass through a body comprised of agents of the various state governments, it makes it much harder for the federal government to usurp the states’ rightful power.
Because the Senate represented the state governments, each state’s senators were charged with jealously guarding their state government’s constitutionally retained powers against unconstitutional encroachment by the federal government.
So imagine if you will, that when Obama pushed his Obamacare legislation through Congress that we had a Senate comprised of senators appointed by their respective state legislatures. Most of the states don’t want to implement Obamacare, and don’t like having their constitutionally retained powers over health care usurped. The senators, being beholden to their state legislatures, would have stopped the nonsense and protected the powers rightfully retained under the Constitution by the states. This is exactly why the founders created the senate as they did.
You see, the founders knew that the federal government could never be trusted to keep its powers in check. This is why the Senate was created as a buffer to give the states a direct veto over a possible federal behemoth.