Fair points TBH, assuming that there is a 1:1 ratio between gross weight and emissions. Is there?
Not an absolute – absolute because of course you can build a car that is low emissions that is heavier than one that isn’t and so on.
But in the real world, where we’re talking about the same car with the same engine efficiency and the same frontal area and the same tyres at the same pressures and so on, clearly you wouldn’t put 300kg of paving slabs in the back and expect it to make no difference.
So why do it with 25 or 40 or whatever of fuel, that you don’t need to. It might not be a linear correlation, it might not be a major difference on a personal level, but it does make a difference.