obviously the weight hasn’t magically disappeared. but the effect i mentioned will distort the calculation of it.
it depends what sort of answer you are looking for here. the tire contact pressure isn’t uniform, due to internal stresses and edge effects in the tire structure. you can integrate the pressure over the contact area, but first you have to know the distribution, which you don’t. this means any result would be approximate to some degree, depending how well you model it.
the boat solution is fanciful, but you allows you to compensate for every physical effect in your calculation. so in theory, you could calculate the EXACT weight, which was the objective of the question when it was put to me. the point is that, as a 'thought experiment', this gives the answer precisely, to arbitrary accuracy, the other method cannot.
cheers, kk