PCYC Queensland chief executive Phil Schultz said first-aid was administered by PCYC staff and other members before Ben was taken to hospital.
"We are deeply saddened by this incident and are offering support to all PCYC Pine Rivers members and staff," Schultz said.
"We will also offer support to family and friends of the young man involved.
"We made contact with Worksafe Queensland (on Tuesday) night and are co-operating fully with their investigation."
Police are assisting Workplace Health and Safety with their investigation.
Ben plays under-15s division 2 rugby league for the Pine Central Holy Spirit Rugby League Club.
On behalf of Pine Central Holy Spirit RLFC our thoughts and prayers are with Benjamin Shaw one of our U15Div2 players...
Posted by Pine Central Holy Spirit Hornets on Wednesday, 27 September 2017
Club president Sharon Hickey said Ben was on life support last night.
"Our thoughts and prayers are with Benjamin Shaw, one of our U15Div2 players who was in a serious incident at PCYC gym late yesterday," she wrote on Facebook.
"He is currently on life support fighting for his life at Lady Cilento ... please take a minute and say a prayer for him and his family."
Reports emerged last night that Ben had been trapped under the weight for 20 minutes.
According to Seven News, Ben weighed 65kg and was lifting 98kg at the time.
He is a student at Pine Rivers State High School.
On Facebook, Pine Rivers PCYC staff wrote that the facility would remain closed until further notice.
