The South paid the bulk of the revenues, between 72% and 83% depending upon where you get your numbers, but virtually all of that money was spent in the North, and they knew it.
This man outlines the disparity in his speech before the South Carolina Secession convention.
From your link, Rhett said this: "The people of the Southern States are not only taxed for the benefit of the Northern States, but after the taxes are collected three-fourths of them are expended at the North."
Only conceivably true if by "the North" you mean any states north of South Carolina.
This site includes a lengthy discussion on antebellum Federal spending, north versus south.
Crunching the numbers shows that overall "the South" came out at roughly 50%, compared to "the South's" total of 30% of US voters.
And this extra Federal spending on "the South" doubtless represents "the South's" over-representation in Congress from the Constitution's 3/5 rule.
So, how should we define "the South"?
Well, Rhett himself was from South Carolina representing the Deep South's planters' views.
In 1860 the Deep Cotton South had about 10% of US voters and shipped 50% of US exports.
So, for Deep South planters an argument might be made, as DiogenesLamp & Rbt Rhett made it, that their representation in Congress did not reflect the full value of their economic contributions.
On the other hand, the Constitution's 3/5 rule did give them gross over-representation, allowed them to dominate the national Democrat party and through it, all of Washington, DC.
In the 1850s the Deep South was the DC "Deep State" by dominating every branch of government from the US Supreme Court to the military.
So where do DiogenesLamp's statistics of "between 72% and 83%" come from?
In sum, "the South" was certainly important economically, but just not as important as they imagined, a fact demonstrated during the Civil War when all commerce with Confederate states ended and yet the Union survived & prospered, doubling it's GDP from 1860 to 1865.