The FIA regulations define "weight" as:
1.9 Weight :
Is the weight of the car with the driver, wearing his complete racing apparel, at all times during the Event.
So it's the car, driver, and all his apparel. Post race everything is weighted, is it critical in one circumstance it is car, driver with apparel, and the other car with apparel, driver?
As far as the technical process, it doesn't make a difference. In public perception and advertising, the drivers seek to keep their helmets on as long as possible to satisfy sponsors who pay big bucks to have their logo on the helmet.