Southern senators were fearful of having more free states than slave states because they did not want the balance of power to tip and them to be overpowered.
During this time, the balance of free states and slave states was very important. If there were more slave states than free states or vice versa, the balance of power may tip and one would overpower the other. Nobody wanted this, simply because nobody wanted to be drawn into unnecessary conflicts. This can be seen in the Missouri Compromise of 1820, which admitted Missouri as a slave state and Maine as a free state. This was so there would continue to be a balance between the two.
Southern citizens and officials were very fearful of there being more free states than slave states. As you may know, the South heavily relied on slavery and if they did not have it, their income would plummet. They were still focused on agriculture, unlike the North which was becoming more industrialized. In order to maintain their plantations, they wanted cheap labor, which they used slavery for. They feared that if there were more free states than slave states, they would lose representation and the free states would try to abolish slavery.
