Back on topic, based on our smallish sample it looks like Honors Colleges and Programs are, on the whole, associated with little to no guaranteed merit money in and of themselves.
We’ve seen a range from $0 up to about $3000/year. Same with alumni-named scholars program participation in individual departments - $0 to $1000/year.
The students admitted to the Honors and Scholars programs may be eligible for a more attractive merit aid offer overall, based on the attributes that got them accepted to those programs, but there doesn’t seem to be a lot of merit aid tied directly to their participation.
The perks seem more in the area of priority registration, priority for internships, inclusion in an LLP/LLC with other Honors students, sometimes (not always) access to a nicer dedicated dorm, smaller classes (1-2/semester and less rote in content than the typical corresponding lower division class), and enhanced research / study abroad activities earlier in the undergrad program.
So once you factor in the added fees, the motivation for participation in Honors is not financial. It’s more about the factors mentioned above, particularly at a very large school.