No charges have been laid and the investigation into the toddler's death could take some time.
Her father Malcolm Fia has posted tributes to his "princess" on social media.
"My baby ... I love you all my life," he wrote.
"You'll always be dad's princess.
He then spoke further about the tragedy.
"I've felt pain before but this pain, this pain I have never felt," he wrote on Facebook about his daughter's death.
"It's getting harder and harder every day realising that this isn't just one bad dream.
"I know you're up there smiling and looking over everyone but dad misses you so much.
"It's hard to process that you're gone but it's what I gotta live with now."
Other family and friends also paid tribute to Arapera.
"So young but touched so many life's with love and joy, rest sweet beautiful lil girl," a loved one wrote.
Another said: "My heart is broken she was so beautiful."
Detective Inspector Warrick Adkin said the toddler had multiple serious injuries which were not considered accidental.
"The police investigation is continuing to establish the full circumstances surrounding her death," he said.
"Enquiries at the Weymouth address are continuing and the occupants are currently co-operating with police."
The toddler's death has rattled neighbours, who said they used to wave to the girl as she passed their house and saw her playing on a small plastic slide in the property's front yard.
One Gibbons Rd resident told the Herald she had left flowers for the family and hoped the community could come together to mourn. She said she also had a young daughter and the death had shaken her.
She said detectives had questioned her about whether she had seen or heard anything unusual.
Are you worried about the safety of a child?
If you have concerns about the immediate safety of a child, call 111.
Alternatively contact your local police station - click her for a list.
Or, contact Oranga Tamariki, Ministry for Children on 0508 326 459 for advice or click here to visit the agency's website for more information.
