+1 on soxmom’s post #2. Even a school that doesn’t have a huge endowment/FA budget (relative to the Andovers/Exeters of the world) will come up with money if they truly want a particular kid.
That said, I recommend looking at the average FA award at any schools that make your “to consider” list. At the school with which I am most familiar, St. Andrew’s in Delaware, the average FA award for the 2015-16 school year was $42,688. Which is otherwise known as a whole lot of money. Another stat to look at is the percentage of the student body who receives aid (to gauge if you will be more likely to receive some…assuming your family qualifies for it).