BPF
More than likely because if the FAA get wind of it they just suspend the pilots license and ask questions later.
UK unless something happens nothing will be said or even looked into. And even if it does the CAA can only take you to court you will still have your license afterwards.
And the fact is nothing really ever happens. In fact if they collected the data there would be a strong case for increasing MTOW of most old training types by 100kg.
The British climate is usually sub ISA and the runways that schools use are substantially longer than required and below 500ft altitude. If you got to a short runway school such as Neitherthope I would imagine they don't take the piss.
Realistically funfly was more than likely over 100kg over weight when they departed and they didn't like it but they survived
Must admit I have got into a tommy not as PIC with a mate both of us over 105kg with full tanks and only really thought about it as we were climbing through 3000ft. 15 deg C sea level no real addition to the runway used. Climb rate 450ft/min.
Its not just the performance you need to worry about though. You put substantially more load on the wings which will then screw with the fatigue life.
But again some of these machines have been getting the same treatment for getting on for 20 years now without wings falling off. Showing how over engineered they were in the first place.
I be worried in modern training types which have much leaner design tolerances.
Conversely a pilot will get lots of abuse for poor RT both from peer pressure and ATC.
with a full family aboard
I suspect that would be still significantly less that two UK rugby playing blokes.
But may be a lot worse safety risk due to as G says the fact that the CoG will be way out towards the dangerous rear end if they have stored the kids in the back.