BOSTON—Emails among athletics, admissions and fundraising officials at the University of Southern California show the school explicitly weighed how much money applicants’ families could donate when determining whether to admit students.

The messages were filed Tuesday in a Boston federal court by a lawyer for two parents accused in the nationwide college-admissions cheating scandal. He claims USC wasn’t a victim of any scheme, but rather based admission decisions in part on expectations of donations from well-heeled families....