i've come across that question before. the answer i was told at the time had to do with putting it on a boat and then measuring the increase in displacement!! (hmmmm - any sane person is obviously going to think of that!) In theory, you could do an accurate calculation of weight, since the shape of the hull is known and the displacement would be large enough to be measured with some precision, however if i had a yacht large enough to float a 747 i'd stock up the bar and sail home from seattle, rather than fly my dubiously weighed jumbo...
johns idea is a good one, although I guess the internal stresses in the tyre structure will support a (probably very small) proportion of the weight, which would not show up in the tire footprint times pressure calculation.
kk