> Can it be addressed with, say, liability insurance premiums (and is it already)?

if it's priced in already, I would guess that it's in a way that doesn't really discourage driving heavy vehicles. if you get in a collision in your SUV but you're not at fault, the people in the other vehicle are more likely to have serious injuries but your insurance doesn't have to pay for it. if anything, the risk is probably distributed across everyone's premiums, unless SUV drivers are more likely to be at fault for some reason.

frankly I'm not sure how best to deal with it. there are a lot of people who would do just fine with a small sedan but are unwilling to drive one because they (correctly) perceive it as less safe. this is of course a negative feedback loop where the average vehicle gets heavier and the incentive to buy a heavy vehicle for yourself increases.

perhaps there could be an additional tax for vehicles over a certain weight with an exemption for people who genuinely need it for work or have a large enough household to justify it.