  To each pair consisting of a saturated fusion system over a $p$-group
together with a compatible family of K\"ulshammer-Puig cohomology classes, one
can count weights in a hypothetical block algebra arising from these data. When
the pair arises from a bonafide block of a finite group algebra in
characteristic $p$, the number of conjugacy classes of weights is supposed to
be the number of simple modules in the block. We show that there is unique such
pair associated with each Benson-Solomon exotic fusion system, and that the
number of weights in a hypothetical Benson-Solomon block is $12$, independently
of the field of definition. This is carried out in part by listing explicitly
up to conjugacy all centric radical subgroups and their outer automorphism
groups in these systems.
