I was under the impression that assumed weights were from time to time reviewed.
Surely this is a case of statistical probability - given (say) 100 passengers (bearing in mind different assumed weights are used for adults and children) the odds are that the assumed weight system will be less that the actual.
The Commander also has the right to have all passengers weighed - I have done so on a couple of occasions in the past (B737 type) and the actual weight in both cases was less than the figure assumed weight would have been.
As far as take off speeds are concerned on the B737 a weight change of 1,000 kgs would affect take off speeds by 2kts so rarely would any weight discrepancy affect speeds by more than one knot although there might be a slight degradation to performance.
What is more important is that hold bags (and probably cabin bags too) are weighed rather than using assumed.
When I flew the A320 for a UK charter airline about 20 years ago we were finding we were quite often getting "Check Gross Weight" from the FMGS after getting airborne. As soon as we weighed all bags this showed we were heavier than we thought and the issue was resolved.