Is this some kind of joke? If the taxes already cover 25% of the expenses then adding 1000x on top means you would tax 249 times more than you need. To make it fair you first have to give truck fuel an adequate tax (so it covers 100%) and then divide this tax by 1000 for light vehicles.
If you think it's a joke you're taking the words far too literally.
"like 1000 times more" is not a full proposal. Yes you would reduce car taxes appropriately. Yes you would figure out the actual amount to balance the budget.
My point is that “it will hurt the poor” is a very old and very tired response to proposals that externalities should be accounted for in the cost of goods.
Part of getting better at helping the poor is helping them directly rather than using extremely inefficient and indirect subsidies on various industries to do so.
Then many trucks could be adjusted to have more axles and lighter loads, saving money on both ends.
The end result is a better system.