schools DO see your rankings and DO count it in their admissions as some are 'yield sensitive' : Tuck, Yale, Stern being the most sensitive. From what I've heard, Tuck #needs# to be #1 for admissions consideration, stern likes #1 but will begrudgingly take #2, Yale is similar.
HOWEVER -- if Tuck admits you and gives you a scholarship, Stern may accept you and try to give you their own full scholarship to steal you away from Tuck. If Tuck doesnt admit you, Stern can admit you but if they gave out all of their scholarships in the first round of admissions, then they wont give you money.
Certain schools have a limited amount of scholarship $$ they give out and as such it is usually done in the first round or two for the most selective schools, schools which are less selective may be able to hold their money over until other rounds and 'be okay' with you ranking them #3
lower ranked schools are more flexible overall
and yes i know it says 'schools do not weigh this is or use it' but... reality is harsh

read over all the old threads and pore through them if youd like
This is Flat Out incorrect.
I have talked with people working in the Consortium as well as adcom from Consortium schools. They all say the rankings have NO impact on your acceptance. In fact, schools don't even know what you've ranked them as until AFTER they have sent out their admissions decisions. The scholarship process begins well after the admissions decisions have been sent. It is only at this point that schools can find out what you have ranked them as.
Hope that clears up any confusion.