Police are trying to determine if a body pulled out of the water on Wednesday is that of the victim, 18-year-old Tyler Clementi.
Paul Mainardi, a lawyer for the family, said Wednesday that Clementi was "a fine young man and a distinguished musician."
A law enforcement official says the student's license and Rutgers University ID were found in a wallet left on the George Washington Bridge on Sept. 22 after two witnesses saw him jump.
NYPD harbor officers recovered the body of a white man clad only in pants, wearing a watch and carrying no identification on Wednesday afternoon. The body was taken to the city medical examiner's office; authorities hoped to use the watch to help identify the body.
Two Rutgers students have been charged with illegally recording Clementi having sex with another male and broadcasting the images via an Internet chat program.
Authorities believe Dharun Ravi and Molly Wei taped two sexual encounters.
A Twitter account belonging to a Dharun was recently deleted, but in a cached version retained through Google he sent a message on Sept. 19: "Roommate asked for the room till midnight. I went into molly's room and turned on my webcam. I saw him making out with a dude. Yay."
Two days later, he wrote on Twitter: "Anyone with iChat, I dare you to video chat me between the hours of 9:30 and 12. Yes it's happening again."
Ed Schmiedecke, the recently retired music director at Ridgewood High School, where Clementi graduated earlier this year, said Clementi was a violinist whose life revolved around music.
"He was a terrific musician, and a very promising, hardworking young man."
Steven Goldstein, chairman of the gay rights group Garden State Equality said in a statement Wednesday that his group considers Clementi's death a hate crime.
"We are heartbroken over the tragic loss of a young man who, by all accounts, was brilliant, talented and kind," Goldstein said. "And we are sickened that anyone in our society, such as the students allegedly responsible for making the surreptitious video, might consider destroying others' lives as a sport."
The Middlesex County Prosecutor's Office has charged Ravi and Wei with invasion of privacy. Ravi, of Plainsboro, was released on $25,000 bail Tuesday. Wei, of Princeton, was released on her own recognizance Monday.
Collecting or viewing sexual images without consent is a fourth-degree crime. Transmitting them is a third-degree crime with a maximum prison term of five years.
About 100 people gathered Wednesday night for a vigil on campus.