Danica also launched a separate legal bid on behalf of their young sons, Lincoln, five, and two-year-old Jack, covering lost earnings, financial loss, funeral costs and damages for the loss of Mr Weeks' luggage.
"The cause of the plaintiff's pain, injury, loss and damage was negligence of the defendant," their writs state.
The family is also claiming for 6 per cent of interest on damages and reimbursement of their legal costs.
The doomed flight went missing on March 8, 2014, shortly after taking off from the Malaysian capital of Kuala Lumpur.
The plane has never been found.
In January last year the Malaysian Government announced all 239 passengers and crew on board were presumed dead.