According to the defense motion, the woman sent Mr. Weinstein hundreds of emails after March 18, 2013, the day prosecutors say Mr. Weinstein forced her to have sex with him.

“I hope to see you sooner rather than later,” one email to him on April 11, 2013, read.

The next day she wrote, “I appreciate all you do for me, it shows.”

On April 17, she wrote, “It would be great to see you later and catch up.”

Five months later, the woman sent an email that read: “Miss you Big Guy.”

Mr. Weinstein’s attorney said in the motion that it appeared the woman wanted the relationship to be deeper, and highlighted an email on Feb. 8, 2017, in which the woman, referred to in court records as CW-1, wrote, “I love you, always do. But hate feeling like a booty call. :).”

In another email exchange, the woman was making arrangements to link up with Mr. Weinstein one evening in 2014. She told the movie producer that she could see him, adding that her mother was with her and would “love to meet him.”

Over the years, the woman also emailed Mr. Weinstein asking that he sponsor her for a club membership in SoHo, and help her with car problems and wrote about a search for permanent housing.

Mr. Brafman said in the court papers that in late May he sought to delay the grand jury proceedings in order to obtain copies of the emails, which were being held as evidence in a bankruptcy proceeding in Delaware involving Mr. Weinstein’s company. Mr. Vance’s office, he said, turned down the request and pushed ahead a grand jury vote on the indictment.