Mrs Beeney, 40, of Willow Close, Etchingham, was killed in the village at 06:55 BST on Monday.
Her mother Maggie described her as "the most beautiful person and the most precious person".
Mrs Beeney was walking to the station with her husband when the electricity generator fell, the BBC understands.
The Army warrant officer, who was based in Andover, Hampshire, died at the scene in Etchingham High Street near the level crossing, Sussex Police said.
The generator fell from a Ford Transit flatbed lorry, according to the force.
Her husband, Rob, was taken to hospital with serious head injuries, where he remains in a stable condition.
A 42-year-old Ashford man has been arrested on suspicion of causing death by dangerous driving and has been bailed until 5 October.
Mrs Beeney's family left flowers at the scene with a card that reads: "For our beautiful and precious Emma, with all our love from Rob, Mum & Dad, Mike, Sharon, David and all the family. In our hearts forever."
Another card reads: "Words are not enough to express how sad we feel to have lost someone in our village under such tragic circumstances."
Mrs Beeney's friend Yvonne Jones said her death was beyond belief.
"It's shocking news - heartbreaking," she said.
"I just can't accept it. Its really, really hard to believe."
Councillor John Barnes, the chairman of Etchingham Parish Council said he was "totally devastated".
"They were young, with their lives ahead of them," he said. "One of them is injured and one of them dead. You just feel so conscious of the tragedy."
He later tweeted: "Etchingham has long-expected an accident in the High Street, but the village is shell-shocked by this loss. Huge sympathy for Emma's family."
Ch Insp Rosie Ross of Sussex Police said: "This was a tragic incident and we are investigating the circumstances.
"We would like to hear from anyone who saw the lorry before the incident or what actually happened."
A woman who died after being hit by a generator which fell from a lorry in East Sussex has been named as Emma Beeney.