He argued that Arps had been sentenced on his extreme views rather than the acts he pleaded guilty to.
The court earlier heard how Arps shared the video with a group of 30 "friends or associates" after the shooting.
Millions of people worldwide from all walks of life had done the same thing, Williams said.
But Arps also had a version of the video modified to have crosshairs and a "kill count" added, which District Court Judge Stephen O'Driscoll said had "glorified" the killings.
It was, in effect, a hate crime against the Muslim community, the judge said.
When he was arrested and asked by police about the victims' deaths, he replied, "I could not give a f***, mate".
His lawyer, Williams, said he had deleted the video as soon as Prime Minister Jacinda Ardern said it was unlawful for people to possess or share it.
Arps remains the only person facing charges of possessing or sharing the video to be named in the media and have his photograph published.
Unlike others, once he is released from prison, he will not be able to keep a low profile "or put his head above the parapet without being noticed", Williams said.
He has no connection with the man charged with the March 15 murders but is now linked to him "because of what happened and how the media has reported that".
The Crown said the District Court judge's starting point was "within range" of the Sentencing Act, with the "creative" element of having a kill count and crosshairs added being an attempt to glorify the attack and "appears to encourage it or encourage others to act in that manner".
At Arps' appeal last week, the Crown revealed that he had allegedly sent "violent" letters from prison to a New Zealand media organisation.
Crown prosecutor Shivani Dayal asked for more time to investigate the contents of the letters and make submissions to the appeal judge, which may be relevant to her decision
The Crown argued that the letters showed Arps' "unrepentant attitude towards the offending", that he remains at a high risk of reoffending, and that a lesser sentence would not be appropriate.
But while Justice Dunningham agreed the letters portray Arps as unremorseful, they only confirm information already provided by the pre-sentence report about his extreme and unrepentant views, and which had been taken into account by the sentencing judge.
"Given the discretion this court must exercise before allowing fresh evidence on a sentencing appeal, I am not satisfied that the letters provide any new relevant information," Justice Dunningham said.
"I therefore do not need to assess whether they are fresh, credible or cogent, and I decline to receive them in evidence for that reason alone."
Williams argued that the Arps material "must be categorised as 'low range'" but Justice Dunningham rejected the argument, as she considers "first person footage taken by a gunman recording the mass killing of innocent people at prayer could never be considered as low range in its degree of offensiveness".
She also dismissed arguments that no harm was done by Arps' offending, and endorsed Judge O'Driscoll's view, that, even if those who received Arps' message were not distressed by it, the public depiction of extreme violence causes "immense distress to all those associated with the victims" of the terror attacks, particularly in this case where the video was distributed so soon after the attacks.
In 2016, Arps was one of a group of men who filmed themselves doing Hitler salutes as they delivered boxes of pigs heads and offal to the Al Noor mosque in Christchurch.
"White power … Bring on the cull," Arps was seen saying in the video.
In that case, he was convicted of offensive behaviour and fined $800.
