They were explicitly afraid of a strong, central executive. There was a very recent -- in fact: current -- example of that exact threat: his name was Abraham Lincoln. In a wider sense, the entire ideology of the Republican Party embodied this existential threat to the notion of state sovereignty. (And whatever else we may say about the Confederates, the gradual but ultimately immense increase in size of the Federal government since the essentially 'minarchist' days of the Antebellum period certainly demonstrates that fears of encroaching Federal power weren't exactly insubstantial.)
What I'm saying is: the Confederates knew that the central power would increasingly be dominated by the North, that (per the Republican Party's essentially neo-Hamiltonian ideals) it would increasingly amass power, and that it would ultimately use this power to abolish slavery (and all other elements of states' rights, but for the Southern elite, slavery was the Big Thing). This looming threat is what prompted secession in the first place, and it's what informed all their revisions to the Constitution: explictly small government, explicitly states' rights, explictly pro-slavery (the Big Thing, superseding states' rights), and explicitly against a too-powerful executive.
From their perspective, it made perfect sense.