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.
On the third day of their stay, Weber, from Baton Rouge, Louisiana, plunged into the water to make his proposal.
His note read: "I can't hold my breath long enough to tell you everything I love about you. But… everything I love about you, I love more every day!"
