HR in Aus here.
It may not be ideal for you but I would definitely look at moving this employee on if he cannot lose the weight. Start by getting I'm to provide a medical clearance for the duties her can perform.
You can write a letter and ask him to bring it to his doctor with the duties he is expected to perform in it and the doctor can assess his suitability for that work. The letter would need to be accompanied by a medical release for the employee to sign that would state he allows the doctor to provide that information requested to you.
Performance managing him is the next step for not performing in his duties and working with his doctor to get him to a place where he can.
The only issue is that the company may be liable for any illnesses associated with his obesity if you take on the approach to help him with his weight. It's a bit muddy, so if I were you I would reach out directly to an industrial relations expert or a lawyer.
It's probably your best bet to terminate his employment.