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Weatherston (34) is to challenge his conviction for murdering his former 22-year-old girlfriend by stabbing and cutting her 216 times in her Dunedin home in January 2008.
His claim he was provoked was rejected by a High Court jury.
At present serving a jail term of at least 18 years, Weatherston was originally scheduled to have a Court of Appeal hearing this week, but it has been put on hold until a new date is set. A telephone conference involving the lawyers is scheduled for Thursday.
Miss Elliott's father, Gil, said: "Goodness knows how long it could go on for.
"And the thing about it is we don't get access to any of Sophie's stuff until it's all heard."
Among Miss Elliott's possessions being held are a diary and her cellphones.
The system allowing the case to drag on upset Mr Elliott, a staunch advocate for victims' rights.
Weatherston's lawyer, Robert Lithgow QC, could not be reached for comment yesterday.