I agree with much of what Brian and Harvey/pri said. Although, I do think the wealth disparity of cities vs country has much to do with the problem (unlike pri), I agree that it is not everything. And Pri’s point is solid that not all federal outlays in states are due to welfare, such as army corps or engineering/defense work, although I have no idea what percent of federal spending that stuff is and how it fits into the whole picture.
Another thought I had which goes to what brian was talking about, is related to the cost associated with low population density. I would assume federal highway funding for a state like S. Dakota is quite high on a per capita basis compared to Rhode Island, but it is beneficial for the whole nation to have I-90 and I-94 running through its borders. Similarly, Farm subsidies are definitely a benefit to rural states, but those subsidies are also a benefit to everyone who buys their product by providing cheaper food (albeit to a lesser degree, and I am no friend of farm subsidies). Etc, etc. It is not immediately apparent what level of federal outlays benefit the nation as a whole, and what level are only useful to the states themselves.
My only point in all this is to show that the map doesn’t really tell you a whole lot. Or at least it is not as hypocritical after first blush.