] Does anyone know whether there was a reverse correlation between wealth and famiy size in JA's time?

The Prices aren't among the real poor: he's an officer, and they have a servant; they are in the middling category. My guess would be that these are the people who produced the largest families. The wealthy could afford separate bedrooms for husband and wife, and the poor suffered from horrible infant mortality.

There were some very large families among the aristocracy, all the same, of which the most notable is the vast number of offspring of George III.

For questions of this sort, I recommend
"The Family, Sex and Marriage in England 1500-1800" by Lawrence Stone