As far as I know, merit scholarships are given only to the elite of each school. A wild guess would be the top 5%, but that is beside the point. What is more important -again, as I understand it- is that almost every school gives them to only the top admitted students... So, even though the average student in Harvard probably turned down merit scholarships in his/her state school, he/she likely didn't make the cut-off for merit scholarships at that top school.
There are other schools that just give aid to all admitted like Mayo and CCLCM, but that doesn't fall into the "merit" category, strictly speaking.
I hear places like Michigan and Chicago also give out a lot of aid, but I couldn't say whether it is merit based or given according to other criteria...