Police were called before the announcement was made.
The Virgin Australia flight was due to depart Auckland at 4:25 pm today, but before they could check in, Wellington women Kerri and Louisa were told they would not be boarding the flight as it was over its weight limit.
They were heading to Rarotonga for a holiday and to celebrate Louisa's birthday on New Year's Eve.
"They said it was a weight issue, but it was pretty clear it was overbooking," said Kerri, who did not want her last name identified.
She said around 15 passengers were affected, but they were not told what the problem was until three police officers were called to the scene.
"They had called them in before they would tell us what was happening," she said. "It made us feel like we were not trusted to behave ourselves.
It was like they were saying 'this group is potentially threatening'.
"I understand that they need to protect themselves and there would be some angry people out there who might get unruly and where that would be necessary, but at the same time, it still makes you feel a little bit stink. "
A spokesman for airport police confirmed officers had been called the scene as they were told "there might be a problem".
"We were called to keep the peace," he said. "We were also called to an Emirates flight that was cancelled that afternoon."
Despite the bad news, none of the affected passengers had been yelling or behaving violently, she said. She had observed that many were on way to visit family members for Christmas -- with December 25 still a day away in Rarotonga.
"There was a little boy, no older than five, who was travelling unaccompanied to see his grandparents for Christmas and he wasn't allowed on," Kerri said.
After a two-and-a-half hour wait at the ticketing counter, the women were told they would not be re-booked for another two days.
They were provided with accommodation at a nearby Holiday Inn until their flight on December 27.
Virgin Australia check-ins are handled by their partner airline Air New Zealand, but staff at the ticketing counter were not aware there had been a problem and deferred queries to an overseas Virgin Australia contact.
A spokeswoman for Virgin Australia said the incident was due to "forecast inclement weather in the region" which meant there were additional weight restrictions in place.
"We apologize for any inconvenience caused to our guests, and will have them on their way as soon as possible," she said.
"Guests who were not able to travel were advised of their recommendation around 30 minutes after check-in closed. Airport security was present throughout this process as a precautionary measure only. "
However, Kerri said communication was poor and the situation could have been handled more effectively.
"The whole way it was handled, there was just no communication for the longest time. Potentially they weren't even telling us the true story of what was happening.