Is the root of the question ‘where is the cut-off for getting financial aid’? as somebody with experience of being at the borderline between qualifying and not qualifying for finaid, the answer is that each school has it’s own zones, and they won’t tell you what they are. Instead you show them what you have & they tell you what (if anything) they will give you.
In the olden days you were either a scholarship student (not a button to your name) or you weren’t (your surname was on the button), but the BSs realized that they were ending up with really polarized student bodies, so they instituted sliding scales that took into account things such as number of kids in ‘independent’ (the polite word for ‘private’) schools so that there was more socio-economic diversity in the student body.
IF that was the root of the question, the only way to know if BS is affordable for you is to do the sums (how much are you comfortable spending), ask a couple of schools what the numbers would look like for you, and compare the numbers.