There is no definitive list of colleges offering more merit aid than previously. Colleges adjust how much money they give (or not) all the time. Scholarship funds can get depleted, colleges and donors create new scholarships, aid amounts are lowered or raised, colleges decide what types of students they want to award scholarships to, and the list goes on and on.
It’s no secret that higher education is struggling right now, but there are a number of lesser known colelges offering good merit awards. Check out a list like this on USNWR. https://www.usnews.com/best-colleges/rankings/most-merit-aid
Look at a site like College Data. Search for the school, go to financial data. The site gives numbers on percentages of students receiving non-need based gift aid and the average amount given. For example, Abilene Christian seems to give a substantial amount of gift aid. Abilene Christian University Tuition | CollegeData
Assuming a student receives gift aid, the parents are still on the hook for a substantial amount of money. You will simply have to start by compiling a preliminary list and looking for information about the kinds of financial incentives a particular school offers. You will need to scour the school website to see the scholarships they have. Another piece of the puzzle is that merit awards are generally given by the admissions office, not the FA office. You have to remember that merit awards are a carrot on a stick to convince students to matriculate.
Even then, many many colleges do not disclose the actual amount of their awards, nor how many are available. For example, Colorado College states they offer the Leadership Scholarship, but not how many are available. Scholarships - Colorado College
Other colleges may be even less transparent and not state the value of a particular scholarship. That could be because it depends on how much money is still left in a given scholarship fund and how many they end up awarding in a given year.
In my time on CC (about 12 years now) I have seen colleges such as Penn State and Syracuse offer numerous great scholarships (merit aid/awards) to students in my region, then subsequently offer very few and only to tippy top students. I’ve seen schools such as F&M offer merit awards, then offer none, and recently, go back to offering some. Some schools that used to be well known for giving generous merit aid have stopped altogether. Some would give more merit aid if a student filled out some additional essays by a particular date, then stopped doing that at all. It changes all the time.
There are colleges such as Berea and Deep Springs that are tuition free. Cooper Union was free for a while, then went back to charging tuition.
Bottom line, you need to do some digging and stay on top of the latest changes in merit awards at a college of interest.
In general, be a great student with really high grades and test scores. That’s the best way to get scholarships, if the college offers them at all. The more selective the college, in general, the less likely they are to offer scholarships (barring a few very high profile scholarships reserved for the cream of the crop at a very few elite colleges.) A private college with a higher acceptance rate might be more likely to offer merit awards to a good student.
If getting merit awards is a necessity to affording college, your student needs to have great grades, bottom line. Be sure to have public in-state schools on the list that your child likes and can afford.