Ivy League and Division III schools don't grant athletic scholarships, but they do award aid based on financial need.
Schools are subject to strict rules regarding scholarships.
Also, they are not obligated to pay your way in full, nor are they obligated to pay for each of your years of participation. Scholarships are granted in one-year increments. Your college may choose to renew your scholarship for up to five years within a six-year period. In Division I and II, a partial qualifier may receive an athletic scholarship under certain circumstances. Students who have not met eligibility requirements may receive need-based financial aid but not aid based on athletic ability.