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I need to have a spare wheel in my trunk or my car doesn't drive properly
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If you add weight, you have more force pushing down your tires but also more inertia to overcome, so it cancels out.
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This is probably not best suited to the aerodynamics section, but it is here now.
But it obviously doesn't cancel out, because if it did then removing the spare wheel would make no difference. The inertia is reduced, there is less grip, both proportionally by the same amount because the tyre grip can be assumed to be linear.
I suppose the question is really, why does a small change in weight/downforce have a big effect on some cars, yet a negligible change in others?
And why doesn't the grip loss balance, less weight at the front, less grip at the front. The only explanation I can think of is weight transfer, cg height, moment of inertia, or maybe tyre pressures too high for the new weight.
To be clear, I don't believe that the sole cause of increased stability in Julian's case was a few kg of downforce, I believe that it is mostly to do with the centres of pressure moving further back, but I think he would disagree.