Most (good) schools do not give merit discounts. They give "discounts" for need-based financial aid only. When you see an ivy that lists as 92k per year has an average cost of 24k that is because 60% get some sort of need-based aid, some pay 0, and 40% do not qualify and pay the full price of 92k. If you make more than 300k you are paying the 92k per year it does not matter if you are hooked or super smart or the top debater in the country there is no discount.
Schools that have trouble filling seats and/or want to attract out of state students offer "merit" to a large section of students, over 50% of those who are full-pay(over 300k) receive discounts. They are not really "merit": many above average, not-outstanding students who cannot get into UVA, VT, or William and Mary because they do not have the scores grades or rigor, get in to Tennessee, Ole Miss, Auburn and get lots of "merit" making those schools net cost around 40k . That is hardly merit when the student is not good enough to get into any of the three top VA schools.
REAL merit is rare full cost of attendance or at least full tuition, offered to fewer than 5% of the incoming class without regard to need(no fafsa no css), typically at Top50ish schools, a few T10s have some. Sometimes it is tied to demographic hooks though that has mostly stopped.
Unpopular private schools throw merit money at over 50% of the attendees. They try to buy students. They are the schools that are in danger with the enrollment cliff. Any LAC below top-20 and Any uni below Top-60 should be highly scrutinized as far as financial security. Look at WVU, they have huge problems, as the flagship nonetheless, and shuttered many departments.