The answer is that weight considerations are of minor concern
to a stationary plant. There is no advantage in a lightweight
fuel to an organism that is not going anywhere. The chemistry
of assembling starch chains from glucose and recovering glucose
again is particularly simple, whereas the metabolism of fats
and fatty acids is more complicated.
Plants store energy in starch because it is especially easy
to get the energy in and out. Animals, which must move about
and carry their fuel supplies with them, find the low energy-per-gram
feature of starch to be a disadvantage. They put up with the
more complicated chemistry of fats to achieve an energy-storage
efficiency only slightly less than that of gasoline.