Weatherald was unbeaten on 112 on day one after a fast-starting NSW were bowled out for 204 before tea at Cricket Central.
Fellow Test aspirant Nathan McSweeney could only manage 16, and the visitors were kept to 5-162 at stumps on Wednesday after NSW quick Sean Abbott took three wickets.
Weatherald was dropped after Australia's shock Test loss to Bangladesh in August, while McSweeney is back in the national team conversation after selectors axed Marnus Labuschagne for the upcoming Test against New Zealand.
NSW duo Sam Konstas and Kurtis Patterson are also in the frame to replace Labuschagne, but both, like McSweeney, squandered their chances to make a statement on Wednesday.
The hosts had won the toss and elected to bat, getting off to a flying start thanks to Ollie Davies (70), who scored 52 off just 36 balls to push his own Test case.
NSW were cruising at 0-81 when a fit-again Jordan Buckingham claimed his first of five scalps - Konstas (24 off 19 balls) charging down the wicket and attempting to clear the infield only to find McSweeney at mid-off.
Buckingham, in his first game of the season after recovering from a hamstring injury, then had Patterson out for a three-ball duck in the same over.
Will Salzmann (three) was the next to fall and the Blues were suddenly at 3-85 when captain Nic Maddinson joined the fray.
Maddinson (47), who played in Australia's first two Tests against South Africa before being dropped for the deciding encounter, was almost dismissed for a duck when he hit his first ball back to Buckingham, who spilt the chance.
Buckingham then cleaned up the lower order after lunch to finish with 5-53 off 14.2 overs.
The Blues have yet to win a Sheffield Shield match after starting their season with two draws and a loss, while South Australia are looking to snap a two-game losing streak for their first win since beating Victoria in their opening clash.
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