When two cars of equal size collide the total damage is approx 2D where D is the damage to either car. Since (in the US at least) about 70% of accidents are two car collisions this suggests an average traffic accident externality of around 70%. So people drive excessively given the risks they impose on others.  The first best solution to this is to tax insurance premiums to capture this externality.  People will drive less and the externality gets internalised.

However if a big car hits a small car the big car gets off lightly and the little car cops it severely. Now the big car imposes a really large accident externality and the small car a much smaller one.  Internalising the externality by encouraging less driving will occur by insurance premiums on big cars being really punitively taxed and on light cars being lightly taxed.

These types of taxes are not very popular and so are often approximated by using distance related insurance charging.  The same principle applies – if you drive a weighty 4-wheel drive or a B-double truck your premium per kilometre should be much higher than if you are driving a small car.  Of course the fixed charge per kilometre also depends on the characteristics of the driver.  A young male should pay proportionately more.  Finally, if you are worried about high taxes inducing people to not insure a very rough approximation to the scheme would be to levy different registration charges by weight of vehicle (as is currently done) then charge a compulsory insurance levy via a premium on fuels.  This isn’t as good since people respond to the levy by using more fuel efficient cars – not the externality targeted here – rather than driving less.