Many or most of the colleges that claim to “meet need” have their own definition of “need” that is not necessarily based on the FAFSA EFC or SAI. Claims to “meet need” are mostly just marketing because of the discretion that colleges have over the definition of “need”.
To get an estimate of financial aid at any given college before applying, use the college’s net price calculator.
Based on https://finaid.cornell.edu/cost-attend/financial-aid-initiatives , home equity is included in parental assets for Cornell’s calculation of financial aid.