Brafman has already sought to cast doubt on the rape allegation, saying that the accuser had a decade-long relationship with Weinstein that continued after the alleged attack. "I was so happy you saw me today!"
At another point, they made plans for him to meet her mother. And in an email in January 2014, she wrote, "you're the one who makes it look good with your smile and handsome eyes".
Some of the messages appeared even more intimate.
Weinstein is facing two counts of predatory sexual assault and two counts of criminal sexual act, as well as rape in the first and third degree.
After saying she had a schedule conflict and couldn't make it to a hotel to see him in February 2017, the woman explained: "I love you, always do".
According to the Los Angeles Times, Brafman's 159-page motion revealed that the woman who is accusing him of raping her twice had "extensive communications" with him for years afterward, and only started to call it rape afterward, in the heat of the #MeToo movement.
"This flawed presentation, we submit, knowingly allowed the Grand Jury to receive a materially incomplete picture of the evidence known to exist in this case, namely the long-term, consensual, intimate relationship between CW-1 (the alleged victim) and Mr. Weinstein", defense lawyers wrote.
They also take issue with other charges against Weinstein on legal grounds, such as being too vague or outside legal time limits, and argue all the charges should be dismissed.
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A spokesman for the New York District Attorney declined to comment.
NY appeals courts have said prosecutors aren't obliged to present grand jurors with all forms of evidence that could favour a defendant, but the courts also have noted that prosecutors are obliged to seek justice and not just convictions.
His team argue prosecutors should have shared the evidence with the Grand Jury that indicted him.
The defence accused Manhattan District Attorney Cyrus Vance of acting in haste, caving under "unprecedented" pressure to indict Weinstein, having been criticized for failing to prosecute him for an alleged groping incident in 2015.
The Associated Press generally does not identify people who say they are victims of sexual assault unless they consent to being identified publicly.
Mr Weinstein's lawyers say the case should be dismissed in its pre-trial stage.
Harvey Weinstein's lawyers want a NY court to throw out sexual assault charges against him. He denies all allegations of non-consensual sex but has apologized for causing "a lot of pain" with "the way I've behaved with colleagues in the past". He is now on a $US1m bail bond and wears an electronic tag.