The unfavorable balance has to do with England's use of Ireland's resources to the detriment of the Irish people. Food, crops were exported to England while the poor Irish people were left to starve.
In "A Modest Proposal," Swift is discussing the unfavorable use by England of Ireland's resources. England, the dominant power, exported Ireland's crops for their own consumption, leaving the Irish, literally to starve. Swift's satire regarding the consumption needs of England, seemingly like a ravenous beast, suggests that the English begin to utilize the children of the poor Irish as their new food source.
What he is talking about, of course, is the fact that England is robbing the Irish of their very survival by removing their food crops, and the disparity between rich and poor is growing larger by the each passing day.
Swift is really making a political statement about the misuse of resources, the tyranny of the English against the Irish and the lack of proper governing provided by Irish politicians. He is also disappointed by the lack of fight against this inequality from the Irish people.
England treated Ireland as they treated the Americans when we were colonies. They took all the best resources of the people and country, and returned shoddy goods. The Irish were treated as second-class citizens who were Catholic (not popular during this time since the monarch of England supported a Protestant faith) and impoverished. Unfortunately, many of the Irish also drank quite a bit, so the English tended to see the drunkenness and poverty as a factor the Irish brought upon themselves...not a situation from which they could not escape. As a result of not being able to pay their rents and bills, the absent English landlord often had their tenants evicted into the streets without regard for children and pregnant women.
The English took and took, but did not fairly compensate. This is what Swift refers to when he speaks of an unfavorable balance of trade. England gets all the good stuff, and the Irish get very little, if anything, of real worth.