The woman's family believes she might have jumped overboard, but the FBI is still investigating whether someone pushed her.
The Mexican Navy said late Monday it had ended its search for Jennifer Ellis Seitz, a Florida journalist, who was reported missing by her husband about eight hours after a surveillance camera captured a person falling overboard on Christmas night. The U.S. Coast Guard also called off its search Monday.
The 36-year-old woman's family said she had "previous emotional issues," but they said there were no outward signs of distress while on the seven-night cruise from Miami.
Seitz's mother joined her daughter and son-in-law on the cruise.
"Jennifer was in a very happy and uplifted mood both before and during the cruise," the Ellis family said in the statement. "She was excited about starting a new job and her future career with a local newspaper. She and her husband had been talking about starting their family."
Seitz and her husband, Raymond, were celebrating their one-year anniversary on the Norwegian Pearl cruise ship.
The ship docked Sunday in Miami. Norwegian Cruise Line said it was cooperating with the FBI.
Raymond Seitz has not been charged with any crime. A message left seeking comment at the couple's house Tuesday wasn't immediately returned. The paving company that employs him was closed until Monday.
The couple met in a weight loss support group; both had undergone bariatric surgery. She chronicled her weight loss journey for an Orlando TV station.
She was also a freelance writer, having written articles for The Tampa Tribune, The Ledger in Lakeland, and an online article titled, "Battling the Bulge Onboard," about how not to gain weight while aboard a ship.
Raymond Seitz was arrested in April on a charge of domestic violence-battery after being accused of head-butting his wife. The charge was dropped after he entered a pretrial diversion program. Records show that she asked the prosecutor not to pursue the case.
Many of the passengers saw them as contestants on an on-board game called "The Not-So-Newlywed Game," modeled after a 1960s TV quiz show.
"They stood out a lot more than other people," Nestor, a retired police officer, told NBC.
Nestor, who appeared on the game show with his own wife, said he ran into Raymond Seitz a day after his wife was reported missing.
"I had given him my condolences, and he had a plastic bag filled with quarters, and he said to me that he was going to the casino to see if he could change his luck," Nestor said.
(This version CORRECTS that Mexican authorities suspended the search late Monday.)