"I continue to fear for my physical safety and the physical safety of my family," Bullock wrote in court papers, TMZ.com reported Monday.
Weldon is scheduled to be released in September after three years in the Middle Tennessee Mental Health Institute, TMZ.com reported.
Bullock obtained a restraining order against him prior to his incarceration, saying he had flooded her with phone calls, faxes and e-mails saying he wanted to be with her.
The actress was followed by Weldon for more than a year as she traveled between California, Texas and South Carolina, TMZ.com said.
"Our primary concern is the safety and well-being of Ms. Bullock and her family," her attorney said in a statement. "Our application to extend the restraining order was filed in order to ensure that safety and well-being."