"Did he say someone might be trying to extort him?" asked Arthur Aidala, for Weinstein. "He said a woman named Rose McGowan," said Anson.
McGowan, an actress and activist, is among those who have spoken out about Weinstein.
Joan Illuzzi-Orbon, prosecuting, asked Anson: "When you spoke to Harvey Weinstein himself, was he concerned that people were talking about his sexual conduct against women?" He replied: "Yes, among other things."
Earlier, the jury heard from a forensic psychiatrist that 85 per cent of victims of sexual assault and rape know their attacker and often stay in touch.
Dr Barbara Ziv, whose testimony helped jail Bill Cosby, the actor and comedian, said an attack by an unknown perpetrator in a dark alley was the exception not the rule, adding: "Another common myth is they will not return to the perpetrator. That contact can vary from texts to maintaining a relationship."
Weinstein is accused of five counts of sexual assault and rape, based on accusations made by Jessica Mann and Mimi Haleyi, both of whom had multiple encounters with Weinstein.
His trial is expected to last until March. If convicted, he could face life in prison.