In the video, Weber presses a hand-written proposal note against the cabin window as Ms Antoine films from inside. He spent more time underwater as he opened the ring box.
Antoine, speaking in a Facebook post, said he "never emerged from those depths".
"It is with the deepest regret that we inform that a fatal accident occurred at The Manta Resort on Thursday 19 September, 2019," the resort said in a statement.
The couple had booked four nights at the resort's underwater room, which lies approximately 250m from the shore.
Costing £1,300 (NZ$2567) per night, the cabin is anchored in water around 10m (32ft) deep.
