the ammount of fuel flowing through the main jet is dependant on the pressure difference between the float chamber and the venturi. The pressure drop in the venturi depends on the sqared airspeed in the venturi and the density.
Airflow (volume) is product of speed and venturi cross section,
Airflow (mass) is product of speed, venturi cross section and density.
So you can state, pressure drop in the venturi (metering the fuel) is product of mass flow and volume flow, divided by two times the squared venturi cross section (later is constant).
So the carburator actually regulates the fuel by the product of mass and volume.
In a CD carburator (i.e. Rotax) cross section of venturi and fuel main jet is coupled by means of a conical jet needle, so these carburators are metering fuel by air mass.