It was very important for Southerners to keep an equal number of senators from free states and slave states in order to ensure that their views in support of slavery were defended in Congress. Southerners feared that if Congress became predominantly "free," they would not be able to defend and protect the practice of slavery.
An example of the difficulty of this balance was the Tallmadge Amendment. This proposed the admission of the Territory of Missouri to the Union as a free state. However, this was not passed in the end, and instead, the Missouri Compromise was passed. The Compromise admitted Missouri as a slave state, while also admitting Maine as a free one in order to maintain this delicate balance between free and slave states.