Jones also had been convicted of similar offences on three other occasions dating back to 1998.
Jones' lawyer Rob Glenday told the court prison would be too difficult for his client, who suffered a serious back injury in 2004, due to his complicated obesity, AAP reported.
Judge Vicki Loury slammed Jones's actions as offensive, threatening and racist.
She said Jones had shown no contrition and provided no explanation for abusing the airline staff.
She sentenced him to 12 months' prison, but then ordered he be released on a $2000 good behaviour recognisance for five years.
Judge Loury said if he harassed people over the phone again he would be sent behind bars regardless of his weight.