It’s unlikely you’ll get a lot more money from an Ivy than from UChicago. UChicago gives merit aid, but the Ivies don’t. Perhaps the uncle of @MurphyBrown 's friend got merit aid, but a lot has changed in 40 years - the Ivy Agreement now stipulates that merit aid (as well as athletic scholarships) are verboten.
In short, the only way an Ivy will give you a lot more money than UChicago is if the need-based packages are very different. That does happen, but more often the gap is a few thousand dollars.