For weak sands 1 kgf/cm2 = 1 TSF is a common minimum. At corrected 6 SPT blow count this normally won't be a very weak sand and so the 1.5 tsf range seems a reasonable allowable compression when the settlement is not to exceed 1 inch. Very weak sands should show lower blow counts and for these even 1 TSF would be too much, and the geotechncal information would show. On the other hand, some called weak sands are not as weak and so the upper 2 TSF range given would be reasonable. But if really "weak" 2 would be a bit too far by traditional practice. Almost any soil where is reasonable to take footings as foundation should allow 1.5 TSF.
Other thing is that to the light of the many things that may happen to weak sands related with water, this cover-all old procedures are simply not enough to describe what at hand. But we can't expect the mere extraction of a value from a table to cover such things as potential liquefaction, that have evolved separate procedures for the checks.