The southern states were well represented but not over-represented. Each southern state had two Senators per the Constitution and Representatives as proscibed. At the insistence of the northern states, some people in the south were only counted as 3/5ths of a person.
And at the insistence of the southern ones, those same people got 0/5ths of the vote or representation in Congress.
In the South those individuals were considered property and not people. They had no rights and therefore no need for congressional representation. As a result the white population was over-represented in the House.