"That's for my mum, and also my uncle who passed away from cancer, and I know he was also very supportive of my lifting, like my mum," she said.
"All the lifting is for them."
Amoe-Tarrant was born in Nauru and lived there until she was 12 years of age.
Her mother died of kidney problems in 2009, so she and her siblings were adopted by their grandparents, who brought them to Australia.
Four years ago, Amoe-Tarrant won a silver medal for her country of birth, and now the 23-year-old has one as an Australian.
"I'm representing both countries and I'm proud to be Australian and I'm also proud to be a Nauruan at the end of the day, so no one can take that away from me," she said.
Amoe-Tarrant says she felt a lot of pressure coming into the Games and carried knee and elbow injuries into the competition.
Spurred on by a rapturous crowd, Amoe-Tarrant summoned everything she had to produce a clean and jerk that secured the bronze medal by 1kg.
"The crowd at the last Games was good. Here it's just amazing," she said.
"They were really the ones that helped me get that second lift [to clinch a medal]."