The North was concerned with the South’s struggling economy because the North and South were back to being part of the same country. Since they were part of the same country, they were also part of the same economy. Northerners were concerned both for altruistic reasons and for reasons having to do with their economic interests.
After the war, the North and the South were once again part of the same country. The enmity, particularly on the side of the North, died down relatively quickly. They then started to care about the South’s economy just as someone from the Western US today would care about the economy of the Southeast.
Perhaps more importantly, they cared because the South’s economy could affect them. With the South part of the US again, the problems of the Southern economy could drag the North down. On the flip side of that coin, improvements in the Southern economy could bring greater riches to the country as a whole. For this reason, many Northerners were interested in investing in the South as they thought that developing that region might be good for the country and for them in particular.