Weary firmed in Doncaster Mile betting, but trainer Chris Waller was non-committal on a start after the import's victory in Saturday's Doncaster Prelude at Rosehill.
Having just his third Australian start, the French gelding positioned closer to the speed than had been his pattern and overpowered leader Leebaz to score by three-quarters of a length.
The winner's stablemate I'm Imposing was another two lengths away third.
Waller will let the dust settle before deciding whether to back-up Weary in next Saturday's Doncaster Mile at Randwick.
"We'll make a decision on Monday afternoon," Waller said.
"It's a big step up and I don't think he's quite there yet.
"It worked out very well today. He's been a bit tricky to get right this horse."
Winning jockey Hugh Bowman said Weary had significantly improved since he rode him to third in a benchmark race at his Australian debut in February.
He believes the four-year-old can be competitive in a Doncaster.
Bookmakers also warmed to his Group One chances after the Prelude win, tightening his quote from $18 into $13.
"I assume he will go to the Doncaster now and he'll be a fair dinkum chance," Bowman said.
Weary's victory was a fitting finale to an emotional day which honoured the memory of jockey Nathan Berry, who died suddenly on Thursday.
The four-year-old is raced by Geoff Grimish, who has been a long-time supporter of Berry.