Just to throw in another option:
How much of those 7 tons can be accounted for by an inaccurate fuel measurement?
I'm aware there is some automatic cross checking between the FOB and fuel used by the engines.
But as level sensors can't be super accurate i imagine especially when the tanks are half full there is a certain error that is normal.
Combined with a load sheet that is a bit off due passengers being fat.
And maybe this airframes empty weight is also off by a bit.
(All those errors adding up to 7 tons seems a bit excessive though)
Was the FAC weight more or less than the FMGC weight?
Either way there should probably be maintenance action to weigh the aircraft and check the AoA sensors.
That should give a definitive answer, should it not?
(Excluding a transient issue which seems unlikely if both sensor roughly agree)