  We present a novel \emph{weakest pre calculus} for \emph{reasoning about
quantitative hyperproperties} over \emph{nondeterministic and probabilistic}
programs. Whereas existing calculi allow reasoning about the expected value
that a quantity assumes after program termination from a \emph{single initial
state}, we do so for \emph{initial sets of states} or \emph{initial probability
distributions}. We thus (i)~obtain a weakest pre calculus for hyper Hoare logic
and (ii)~enable reasoning about so-called \emph{hyperquantities} which include
expected values but also quantities (e.g. variance) out of scope of previous
work. As a byproduct, we obtain a novel strongest post for weighted programs
that extends both existing strongest and strongest liberal post calculi. Our
framework reveals novel dualities between forward and backward transformers,
correctness and incorrectness, as well as nontermination and unreachability.
