State governments were much smaller during this period with revenue streams to match (no income tax to speak of, for starters). Further, the trend in economic thought during this period was toward liberalism, meaning reducing government involvement in economic affairs. I haven't heard of a government economic subsidy pre-Civil War.

Next, purchase from where? The importation of slaves was banned following 1808. Setting aside the inhumanity of slavery for a moment, this was a positive for slaveholders whose wealth increased with the value of their slaves.

Individual owners did, shall we say, encourage slave reproduction. This meant both encouraging slave families and the widespread rape of slave women. But this had more to do with increasing monetary value and labor output than increasing representation in Congress. Before anyone asks, I have never seen evidence of professionalized slave "breeders" whose focus was on that rather than agricultural production.

Finally, I doubt southerners saw much point in even trying. The North had a huge population advantage throughout the antebellum period and even, say, matching their growth with slaves at a 1:1 ratio would have put them way behind (three-fifths) and all. Add to that Southern concerns about a slave population becoming too big to control, a society based around agriculture (low population density), and the fact that maintaining a balance in the Senate was a much more expedient path to federal influence, and I'm not surprised I've never really seen this discussed.