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Gross vehicle mass is the maximum operating weight of a vehicle as specified by the manufacturer. It doesn't include any trailers - gross combined mass is the term for that.
Included in the GVM are the vehicle plus any fluids (fuel, brake fluid, water, etc), accessories, driver, passenger and any goods you are carrying in the vehicle. Therefore a vehicle will have a dry weight (what it weighs on its own without fluids), a kerb weight (what it weighs on its own with all fluids at recommended levels and the fuel tank full) and a GVM which is the maximum weight it is designed to take. The difference between the dry weight and kerb weight depends on the size of the fluid tanks, especially the fuel tank.
The gross vehicle mass minus the kerb weight and the weight of any passengers gives you the maximum weight of any cargo you can carry.
Light vehicles by law cannot exceed 3500kg GVM. Heavy vehicles are over 3500kg GVM.
When a vehicle is produced, its components are created and/or chosen to withstand certain stresses. A heavier vehicle puts more stress through critical components which can cause them to either fail, or cease to be as effective. The main affected components are:
Brakes - the heavier the vehicle, the more braking energy it takes to stop it. A vehicle with insufficient brakes (one that is 'under-braked') will suffer brake fade more quickly and may not be able to stop effectively
Clutch - the strength and size of the clutch help define the ability of a vehicle to transfer the power of the engine into forward motion. If the vehicle is too heavy, especially on steep hills, the clutch could slip which means rather than power getting to the wheels, friction is burning off the clutch plate
Suspension - a vehicle's suspension is designed to leave enough suspension 'travel' (potential absorption left in the spring and damper). A heavier vehicle will compress the springs and dampers making the suspension less effective
Safety cocoon - a vehicle's crash absorption is, in part, designed around its weight so that crash impact energy can be channelled into the most appropriate places rather than through the driver.
Tyres - car tyres are only manufactured to withstand certain strains and stresses through them. The forces through components like tyres is magnified exponentially as weight increases.
Additionally, road wear can be increased as heavy vehicles are often designed with road-friendly suspension and appropriate tyres to help minimise the effect of the weight of the load on the road. Exceeding these recommendations can accelerate damage to road surfaces.