With SA heading for a hung parliament, Dr Such and fellow independent Geoff Brock are yet to announce whether they will back Labor or the Liberals to form a minority government.
Dr Such is now believed to need to take extended sick leave from parliament although the nature of his health issues has not been disclosed.
He has been out of contact for most of the past week after talking to both Mr Weatherill and Opposition Leader Steven Marshall in the days after the March 15 poll.
"I am concerned for Dr Such's wellbeing and I have extended my best wishes to his wife and offered my support," Mr Weatherill said in a statement on Saturday.
"We wish Mr Such a speedy recovery and support his family's request for privacy."
Labor could govern with just the support of Mr Brock but if he decides to back the Liberals it would leave support for either side in the house tied at 23 votes each. That could potentially result in a fresh election.
However, it remains unclear whether Dr Such could still enter into an agreement with either party to give more certainty.
Mr Brock is reportedly taking constitutional legal advice.
Dr Such is now believed to need to take extended sick leave from parliament although the nature of his health issues has not been disclosed.
He has been out of contact for most of the past week after talking to both Mr Weatherill and Opposition Leader Steven Marshall in the days after the March 15 poll.
"I am concerned for Dr Such's wellbeing and I have extended my best wishes to his wife and offered my support," Mr Weatherill said in a statement on Saturday.
"We wish Mr Such a speedy recovery and support his family's request for privacy."
Labor could govern with just the support of Mr Brock but if he decides to back the Liberals it would leave support for either side in the house tied at 23 votes each. That could potentially result in a fresh election.
However, it remains unclear whether Dr Such could still enter into an agreement with either party to give more certainty.
Mr Brock is reportedly taking constitutional legal advice.