SYDNEY: Weeks, who was based in the West Australian city of Perth, was one of 239 people on board the Boeing 777 Kuala Lumpur-Beijing flight when it disappeared on March 8, 2014.
Next-of-kin had started to file lawsuits over the jet's disappearance as a two-year deadline approached last week, with some hopeful the court scrutiny could shed light on what happened to the ill-fated flight.
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Under international agreements, families have up to two years to sue over air accidents.
Weeks' wife, mother, brother and sister were separately suing the flag carrier in the Supreme Court of Western Australia, according to Perth's The Sunday Times, citing five writs lodged on March 4.
They were seeking compensation for "personal injury, loss and damage" suffered as a result of "sudden shock" and "mental harm" after the disappearance, the Times said.
"The cause of the plaintiff's pain, injury, loss and damage was negligence of the defendant," the newspaper cited the writs as saying.
A fifth writ was filed on behalf of Weeks' two children, the report added, without disclosing the amount of damages sought.
Sara Weeks, his New Zealand-based sister, told TVNZ's ONE News Sunday she just wanted to know where the plane was.
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Malaysia Airlines also faces legal action elsewhere. In Beijing, relatives of a dozen Chinese passengers filed suits against the airline, Boeing, Rolls Royce and others last week.
The latest legal claim in Australia came as a piece of debris found by a South African holidaymaker in Mozambique in December was to be sent to Australia for analysis, South African officials said Friday.
Other pieces of debris found earlier this month have yet to be confirmed as from the missing jet.
Australia is leading the search for MH370 in the southern Indian Ocean. The hunt is expected to wrap up in June-July if the aircraft is not found in the target zone of 120,000 square kilometres (46,000 square miles).
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No crash site has been located. So far, only a wing fragment that washed ashore on the Indian Ocean island of Reunion last July has been confirmed as being from the plane.