The government gives some Hareidim money in order to influence them and to try to pull them off the derekh of the “pure” hareidim (such as Satmar) who oppose the medinah. As the hareidi community is largely funded by money from overseas, stimulating it actually helps the Israeli economy since it attracts investments, business and transfer payments from overseas.
The Americans give Israel money for several reasons. A big one is to support jobs in America (by subsidizing Israel purchases of American made goods which could more easily be produced in Israel, albeit at a higher cost). It also addicts the Israelis to American money and gets them to do America’s bidding in the middle east.