Sediment preserved in drill cores retrieved from the ice showed that while these mass collapses had happened every couple of hundred years, the melt events could occur in just a decade.
"It's like an earthquake - for a long time, nothing happens, but when it does, boom - it happens all at the same time," he told the Herald.
His study gave fresh cause for concern for scientists battling to better understand the link between Antarctica and climate change.
Before the paper was published in the leading journal Nature this year, it was generally believed that Antarctica's ice sheet had contributed comparably little in sea level rises during the period.
"Our record shows a very different scenario," he said.
"This is the first time we have actually been able to obtain a record that gives you an integrated message of what was going on during these 10,000 years."
The study also shed light on Antarctica's part in the so-called Meltwater pulse 1A event, between 14,300 and 14,700 years ago, when the globe's sea level rose a dramatic 20m in just a few hundred years.
"There has been a long-standing debate in literature as to whether Antarctica contributed to that event or not," he said.
"While all the field data so far said it hasn't, we have been able to provide the first hard evidence that it potentially contributed a substantial part of it."
In this event and others, the bulk of historic sea level rise had been attributable to North Hemisphere ice sheets that no longer exist today.
But metres of sea level rise could still come from a collapse in Antarctica.
Past melting events were driven by warmer ocean waters eating away at ice shelfs, and these processes were being observed today as the planet warmed.
"The ice sheets are collapsing, that's what we have known already for a few years, but recent data has shown that some ice sheets are now beyond the point of no return - this will keep going for decades and centuries, there is no stopping it."
Under present sea level rise scenarios, many coastal areas in New Zealand were predicted to face a greater threat from higher tides and storm surges.
Professor Tim Naish, the director of Victoria University's Antarctic Research Centre, said the UN's Intergovernmental Panel on Climate Change (IPCC) estimated a sea level rise of a metre by the end of this century.
"What we now know from Michael's work is that the Antarctic ice sheet itself is capable of producing up to a metre per century - and perhaps a bit more," he said.
"It's pointing toward the possibility that the IPCC estimates may be a little conservative if we get one of these collapses."
Dr Weber is among 950 scientists attending the Scientific Committee on Antarctic Research's Open Conference, hosted this week in Auckland.
* To find out more about what's happening this week, visit here.
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Why our oceans hold climate clues
Our oceans hold the key to understanding climate change, says a top scientist in town this week.
US oceanographer Dr Steve Rintoul, of Australia's Commonwealth Scientific and Industrial Research Organisation, is internationally recognised as a leading authority on the circulation of the Southern Ocean and how it affects global climate systems.
As more than 90 per cent of the extra heat that has been absorbed by the Earth had gone into warming up the oceans, it was oceans that provided critical indications about climate change, he said.
"We know that the oceans are changing - we can measure that - and modelled projections of what will happen in the future suggests that oceans may be less effective at slowing the rate of climate change in the future."
When looking at impacts of warmer oceans, there were few places as important as Antarctica.
"When the ice sheet flows out on to the ocean from Antarctica, it exposes its soft underbelly, and the heat from the ocean can melt that floating ice," he said.
"Once that floating ice melts, the ice that's on top of the continent can flow into the sea, and that increases sea level."
Scientists drew on factors such as water temperature, salinity and acidification to look for changes in oceans, yet attempting to simulate the interaction of a warmer ocean with the ice shelf remained one of the biggest challenges to climate science.
"That's why the Antarctic ice sheet is still the nost uncertain aspect of future sea level rise."
