Weather stalls search for AirAsia black boxes; first victim buried

* Dozens of divers wait for weather to clear

* Sea expected to be calmer next week

* Data shows plane climbed steeply before disappearing (Updates number of bodies found, adds first funeral, details)

By Fergus Jensen, Gayatri Suroyo and Charlotte Greenfield

PANGKALAN BUN/SURABAYA, Indonesia, Jan 1 (Reuters) - Heavy seas stopped divers reaching the possible wreck of an AirAsia Indonesia jet off Borneo on Thursday and an aviation official said it could be a week before the black box flight recorders are found.

Nine bodies have so far been recovered from the Airbus A320-200, which crashed on Sunday en route to Singapore from the Indonesian city of Surabaya with 162 people on board.

The bodies were brought in numbered coffins to Surabaya where relatives have gathered for identification. AirAsia Indonesia's CEO Sunu Widyatmoko was seen weeping when authorities handed over the body of the first victim, Hayati Luthfiah Hamid, to family members at a Surabaya hospital.

Hamid, 49, was buried on Thursday before sundown in the suburb of Desa Sawotratap, a few kilometres (miles) from the city, at an Islamic ceremony attended by relatives and neighbours. Three members of her family were also on board the plane.

"Their house has been in a panic since Sunday," Umaroyah, a neighbour, said. "Everyone in the neighbourhood knows someone who was on that plane."

Searches on Thursday spanned an area of 13,500 square km (5,200 square miles) involving 19 ships, four helicopters and five planes, said Fransiskus Bambang Soelistyo, head of Indonesia's Seach and Rescue Agency.

A search and rescue pilot has spotted a large shadow in the sea, which rescuers believe may be the wreckage, but they have made clear the sighting is not yet confirmed.

"Until now, there hasn't been a confirmed finding or sonar image of the plane body under water," Soelistyo said.

Forty-seven divers are on standby to investigate.

"I am hoping that the latest information is correct and aircraft has been found," airline boss Tony Fernandes tweeted on Thursday. "Please all hope together. This is so important."

Toos Sanitiyoso, an air safety investigator with the National Committee for Transportation Safety, said it could take a week to find the black box. Committee head Tatang Kurniadi said the focus of the search, once the waters had calmed as expected in five days, was around the shadow.

"We are backtracking from where the wreckage was found to where the plane had its last reading and that is the focus of our search," Kurniadi said. "The depth around here is 50 metres. No specialist equipment (is required). Divers can go get it."