The A320F weighs it's self when it is airborne only when slats are retracted aircraft speed is 250kts or below and the alt is 14500 or below, it does this via the FAC which takes it's inputs from fuel flow and alfa. This is memorized and updated through out the flight.
This is very relevant on the PFD as it is from this information that "coffin corner" is diplayed, even if the aircraft is a lot lighter it will cause the systems to react as if it is at the calculated weight (proctection activation)
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Gravity always wins....