Errors
Reading the postings, it seems that people think that the risk only lies in reducing thrust - not so!
Even if you would use full thrust on every take-off, if you have determined the associated speeds with the Zero Fuel Mass, instead of with the Take Off Mass, you will probably scrape the tail on rotation. Granted, it will happen not so near the departure end of the runway, but still the airplane will be damaged.
As for self weighing aircraft: they do exist! Many cargo aircraft have such a system. Not terribly accurate, but it should provide protection mainly against gross Centre of Gravity errors. However, if such a system is u/s, aircraft dispatch will be allowed according MEL - and then, safety is provided, as on any other aircraft, by rigorous procedures.