Despite Kate Winslet’s glowing performance in Titanic, the role came at a cost. Winslet opened up about fat-shaming comments she received from reporters who fixated on her weight as she graced red carpets around the Titanic premiere, in a 60 Minutes interview released Sunday.

“It’s absolutely appalling,” Winslet said. “What kind of person must they be to do something like that to a young actress who is just trying to figure it out?”

At age 20, Winslet was cast to star in Titanic, opposite of Leonardo DiCaprio, which banked...