The order of protection is to remain in place for three years and covers Bullock's infant son Louis and her ex-husband Jesse James's three children -- Chandler, Sunny and Jesse Jr.
Weldon, 41, was first arrested for stalking Bullock in 2003. He was subsequently hospitalized for mental illness, TMZ said.
Bullock's attorney filed court documents last month seeking a renewal of the protective order she first obtained seven years ago.
In a report last month, "Entertainment Tonight" quoted the paperwork as saying Bullock has accused Weldon of "following her to California to Texas to South Carolina, and then back to California ... He sent numerous e-mails ... indicating, among other things, that he wants to have a relationship with her."