An Environment Court appeal hearing began in Oamaru on Monday after a decision last year by Otago Regional Council and Waitaki District Council to grant the project resource consent.
Holcim New Zealand wants the option to build at Weston if it decides to move its operations from Westport.
But three appellants disagreed with the councils' decision, including the Waiareka Valley Preservation Society and the Kakanui Riverwatch Society.
Holcim has itself lodged an appeal challenging some of the conditions imposed in the councils' decision.
The appeal hearing will run for four days.