My company is a storage and plug-in facility for fully loaded refrigerated containers with meat and fish in Riga, Latvia. These containers come in by ship from the U.S., UK, and many other parts of the world. We hold them, keep them cold, and then ship them onward by truck to Russia.
The maximum loaded weight of a 40' container is 32,000 kg, and the accompanying bills of lading filled out by the sender or his agent rarely state that the cargo is over 25,000 kg. Yet our electronic scale with a print-out half the time shows that the cargo weighs up to 10,000 kg past the 32,000 kg maximum.
The whole truck, once it reaches the Russian border, is weighed. Fines of $250 per ton overweight are not unusual. Overweight trucks will eat up the road they drive on, but the weight is really not that critical to safety.
However, if a sender, or his agent falsifies a bill of lading or a waybill on a weight-sensitive airplane, then I would consider it criminal.
I'm sure that in airline freight operations not every piece of cargo is put on a scale and weighed.
If the customer declares that a crated lawn tractor weighs 300 kg and a wooden crate of frozen fish 150 kg, the airline will probably take their word for it if it is so stated in the bill of lading.
The bill of lading is actually an accompanying document of "sale" which is needed for the end customer to retreive his merchandise. The wooden crate or the steel tub is probably not included in the bill of lading, because in customs, the buyer only pays duty for the product -- and not the packing.
That's how things can go wrong. There are many other tricks in international shipping which I won't go into now, since you're probably already bored.