The duo surged to centuries as the Redbacks piled on the runs to finish the opening day 1/359 after winning the toss and electing to bat.
Weatherald ended the day unbeaten on a career-best 195, while Hunt scored his maiden first-class ton in only his fourth first-class match before being dismissed in the final hour for 132.
The openers put on a mammoth 293 runs, eclipsing the long-standing first-wicket Sheffield Shield partnership record for South Australia of 281, set 52 years ago by Les Favell and John Causby.
It was an impressive performance given SA lined up without senior players Travis Head and Alex Carey, who are both on Australia A duty in the three-day match against Pakistan in Perth.
Tasmania had few answers to SA’s blazing start, with medium-pacer Lawrence Neil-Smith (1/74) the only bowler earn a breakthrough.
Weatherald ended the day just shy of his maiden first-class double century, having reached the boundary 29 times in a 275-ball knock.
Experienced batter Callum Ferguson will resume alongside the left-hander on 20 on Tuesday.