Test and Queensland opener Usman Khawaja dropped Weatherald at first slip off the bowling of Jack Wildermuth when the Tasmanian had made just three on Saturday at Allan Border field.
Weatherald took full advantage of his life, hitting two boundaries in the same over.
The Tasmanian opener went on to make 66 from 99 balls to continue his strong form.
He partnered with captain Jordan Silk to rescue the visitors' innings after Silk's decision to bat first looked to be backfiring horribly.
Reeling at 3-33, Tasmania steadied and were 6-299 at stumps. Silk led the way with 104 and Brad Hope made 76.
Weatherald is coming into Ashes selection calculations thanks to his run of form.
He is the reigning Shield player of the season and made 183 in July for Australia A against Sri Lanka.
He hit eight boundaries and had a crucial 80-run stand for the fourth wicket with his captain before Michael Neser took a sharp reflex return catch with one hand.
Silk went on to make his 104 from 170 balls and was filthy with himself when he was also out caught and bowled to Mitch Swepson.
The spinner's catch was much more straightforward thanks to a leading edge.
Wildermuth was eventually rewarded when he trapped Hope lbw, ending his 171-ball knock.
Jake Doran (25) and Nikhil Chaudhary (nine) were the not-out batsmen, while Neser (2-53 from 18 overs), was the only multiple wicket taker.
Tasmania suffered a blow when Australian allrounder Beau Webster was ruled out of the game because of an ankle injury.
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