The fatal shooting took place at a family gathering held to mark the 15th anniversary of the death of Grannon's son, Andrew Grannon, and the incident has driven a wedge through the family.
Stanley's mother Jenny Dees said Grannon, her grandfather, was "once respected in the family" but claimed he had not shown any remorse in the 11 months since the fatal shooting.
She added: "Not once did he say sorry. Now, if he did it would be meaningless - and too little too late."
Stanley's devastated father Andrew Metcalf also took to the stand and said: "On the 26th of July our little world came crashing down.
"Stanley, my son and best friend, had his life taken away. Every morning and every night I go into Stanley's room and still tell him 'you're my best friend and I love you'.
"There's no reply, and kissing his pillow is not quite the same as kissing your son goodnight.
"The last question Stanley asked was, 'Grandad, why did you shoot me?'. So I'd like to ask the same. Sam - why you take my little boy away?"
Prosecuting, John Elvidge QC said: "The crown is not suggesting the defendant deliberately killed his great-grandson, but by firing the rifle in close proximity to Stanley he was grossly negligent."
Mitigating, Paul Genney told the court: "These are my instructions – he held the rifle and squeezed the trigger to see if it was loaded whilst pointing the rifle at the child but, of course, not deliberately."
Mr Genney said Grannon was "particularly concerned" about the issue of remorse. He told the court: "He instructs me he has been reluctant to communicate with the parents and the mother because in the early stages of the ongoing police investigation he was told that would be an inappropriate thing to do, probably wrongly."
Mr Genney added Grannon feels remorse and "blames himself totally" and said the "irretrievable division between the family has compounded the tragedy".
Sentencing Grannon, the judge, Mr Justice Lavender said: "You ended a young life and you brought lifelong grief and misery to his parents and to the whole family.
"Tragically, this happened when the family had gathered at your home to mark the 15th anniversary of the death of your son, Andrew.
"July 26 this year will mark the anniversary of two deaths instead of one.
"No sentence I impose can bring Stanley back. No sentence I impose can undo what you have done and heal the rifts in your family.
"In all circumstances, what you did was obviously a very dangerous thing to do. Why on earth did you do it?
"I have read your statement and I readily accept that your remorse for what you did to your great-grandson is genuine and profound, although you have not succeeded in conveying that to your granddaughter and her family."
'Our world has changed forever'
During the hearing, in an emotional victim impact statement, Stanley's mother Jenny Dees said: "Our whole word has changed forever.
"It is unbearable, we struggle to live, to eat and breathe. Nothing will make this better, our hearts are totally broken.
"The pain in my heart is unbearable, I cry and cry, and sometimes I think I am not going to stop.
"The only reason I'm still here is because of (Stanley's twin sister) Elsie. Life is so hard to carry on with. Everything seems so pointless. Our family is broken beyond repair."
How did a great-grandfather shoot dead his great-grandson?
Stanley Metcalf had attended the family gathering with his twin sister Elsie, mother and grandmother at Grannon's home in the village of Sproatley near Hull, East Yorkshire, when the incident happened.
The boy was taken to Hull Royal Infirmary with serious injuries after the pellet made a hole in his abdomen, but tragically died after resuscitation was stopped just before 5.30pm.
Stanley had asked to see Grannon's gun which he was in the habit of keeping loaded while stored in a cupboard, the court was told.
The youngster's mother, Jenny Dees heard a loud bang and ran into the kitchen where she saw Stanley bent over clasping his stomach.
He was then carried outside by Miss Dees who initially thought he was play acting but she lifted his top to see a small hole the size of a 5p piece in the left side of his abdomen.
Retired shipbuilder Grannon accompanied Stanley in the ambulance, where the youngster went into cardiac arrest on the way to hospital before he died two hours later.
Paramedics described Grannon, known as Grandad Sam within the family, as "extremely upset" and "shell-shocked".
A post-mortem found Stanley died as a result of a "single penetrating injury to his abdomen", which damaged his bowel and a major artery in his pelvis, causing massive blood loss.
The .22 air rifle - which shot and killed Stanley - was purchased for £90 by Grannon five years ago after he responded to an advert in a local newspaper.
Grannon upgraded it by adjusting a spring mechanism which made it more powerful and meant it needed a licence.
He told police the reason he had not applied for a certificate was because he knew he wouldn't be granted one due to the limited use of his right arm as a result of an accident some years ago.
Grannon pleaded guilty to the manslaughter of Stanley and the possession of a firearm without a certificate last month.
He was jailed for three years at Sheffield Crown Court on Tuesday. He was also given four months for possession of a firearm without a certificate which will run concurrently.
