We compute the weighted enumeration of plane partitions contained in
a given box with complementation symmetry where adding one half of an
orbit of cubes and removing the other half of the orbit changes
the weight by 1 as proposed by Kuperberg in [8,pp.25/26].
We use nonintersecting lattice path families to accomplish this for
transpose-complementary, cyclically symmetric transpose-complementary
and totally symmetric self-complementary plane partitions.
For symmetric transpose-complementary and self-complementary plane
partitions we get partial results and for cyclically symmetric
self-complementary plane partitions we have a conjecture.