Their son Aled Sion Davies, who was one of the brightest stars of London 2012, is going for gold in the F42 shot put at the Paralympic Games.
He is the current world record holder and world champion and won a Paralympic bronze in London as well as discus gold.
"The pressure is enormous," Mrs Davies said.
"He's had golds all season and, obviously, everyone thinks, 'well, yes, he'll get gold here' - but we'll see."
Aled has been working harder than ever since London, his father explained.
"Seven days a week he's been training, and had to focus completely on things like diet and building his strength."
Reflecting on their son's successes, the Bridgend couple said it was hard not to get emotional.
The 25-year-old was born with hemimelia of the right leg, which meant his fibula was missing.
He had to have regular operations up until the age of 12 and wore a special leg brace to be able to walk.
Mrs Davies said: "He was the most beautiful boy. Everyone at the hospital would comment, and yet he had this deformity.
"It seemed like the end of the world.
"And you have to remember that the treatment available then wasn't like it is now - prosthetics and so forth.
"Initially, they wanted to amputate to his knee."
The couple opted for an alternative, where Aled would spend regular periods every year in hospital until he was around 12-years-old.
"From all the pain and suffering he's had - times where we had to hold him down to clean the pins of his leg frame - to see where he is now, I just couldn't be prouder," said his father.
Now at his second Paralympics, Aled's girlfriend, Jessica Beeken, said he wanted to "go out there and show everyone the hard work he's put in".
And winning gold?
"It would be amazing," she said. "Every single day he's been pushing his already broken body to the limit.
"He wakes up in pain, but he's never once doubted that this is the right thing to do.
"It's not football, it's not rugby, they don't get paid masses.
"He does it because he loves throwing and has been doing it since he's was a teenager.
"That's why the Paralympians inspire me so much. They do it because it's their passion and that's quite amazing."
When Hugh and Jacquie Davies take their seats in the Olympic Stadium in Rio on Monday they say they will feel "nervous" and "horrendous" but "beyond proud".