Search and rescue crews from the Vietnam navy were last night looking for traces of the flight, which was carrying 227 passengers, including two babies, and 12 crew.
There were unconfirmed reports it had crashed in the South China Sea, but at press time last night, Malaysia Airlines had not confirmed a crash.
Weeks, who moved to Perth in 2011, was en route to Mongolia where he had taken up a new job at the start of the month.
His wife Danica told the Herald on Sunday that she had dropped him at Perth Airport on Friday to catch a connecting flight at Kuala Lumpur with Malaysia Airlines.
She was too distraught to comment further.
The pair have two young sons, Lincoln and Jack. Lincoln was born during the chaos of the first Christchurch 7.1 magnitude earthquake in 2010.
He was among 21 babies born on the day, setting a record for Christchurch Hospital for the highest number of births on a Saturday.
At the time, Danica Weeks told One News that it was amazing they'd got through two traumas in one day. "It was sort of like 'gosh did we cause this, is this part of it, does the earth move?"' she said.
Paul Weeks said he would tell his son Lincoln that his birth had caused the earthquake.
Weeks attended Aranui High School in Christchurch before studying at the University of Canterbury.
Wang's distraught family members gathered last night as details emerged about the tragedy.
"We're still waiting for the information to come out," Wang's nephew Ned said.
He added they were closely following news reports of the lost aircraft. "We don't want to talk about this at this very moment because my aunty really needs to get her rest," he added.
He said the Ministry of Foreign Affairs and Trade had been in contact. It last night confirmed it was providing consular assistance to the families of the two New Zealanders listed as onboard.
Prime Minister John Key last night said: "Our thoughts are with all families of passengers on Flight MH370 as they wait for news."
Radar data posted on aviation websites suggested a steep, sudden descent of the aircraft before contact was lost. There was no indications that pilots had sent a distress signal.
The aircraft was last seen about halfway between Kuala Lumpur and Ho Chi Minh City, in southeast Vietnam.
A Malaysian diplomat in New Zealand said information was sketchy. "We are praying for the best outcome," the diplomat said.
Flight MH370 departed Kuala Lumpur at 12.41am (5.41am NZT) and was expected to land in Beijing at 6.30am (11.30am NZT).
The passengers were of 14 different nationalities with Chinese making up 152 of those on board. There were also six Australians on the doomed aircraft.
A list of passenger names from flight MH370 was made available by Malaysia Airlines last night.
Kiwi pilot and aviation commentator Peter Clark was "extremely shocked" to hear a Boeing 777 was in trouble. "It's a fantastically designed, strong aircraft.
"That airline is very important to New Zealand. It operates from here to Kuala Lumpur using the same type of aircraft."
A Malaysia Airlines flight is due to depart Auckland Airport at 2.30pm today.
Last night the flight was scheduled to go ahead.
