Groton’s endowment is almost 4x the size of Emma Willard’s. The size of the student body is comparable.
For Emma Willard, increasing the number of full tuition students means the school appeals to parents who can choose nearly any school. That matters, because it’s like canaries in the coal mine for the strength of the overall program.
A “high discount rate” is not seen as a sign of strength for a school or college. https://www.insidehighered.com/news/2016/05/16/discount-rates-rise-yet-again-private-colleges-and-universities
As it is, Emma Willard awards financial aid to a larger share of the student body–46%, than Groton does–39%. Groton is able to offer larger awards, according to what I find on the web. More Groton students are full-pay domestic students than Emma Willard students.
I don’t compare my choices in housing to Bill Gates. I don’t think we should fault a very good school for not having the resources of one of the wealthiest schools in the nation.