  We study the Cauchy problem for the isentropic hypo-viscous compressible
Navier-Stokes equations (CNS) under general pressure laws in all dimensions
$d\geq 2$. For all hypo-viscosities $(-\Delta)^\alpha$ with $\alpha\in (0,1)$,
we prove that there exist infinitely many weak solutions with the same initial
data. This provides the first non-uniqueness result of weak solutions to
viscous compressible fluid. Our proof features new constructions of building
blocks for both the density and momentum, which respect the compressible
structure. It also applies to the compressible Euler equations and the
hypo-viscous incompressible Navier-Stokes equations (INS). In particular, in
view of the Lady\v{z}enskaja-Prodi-Serrin criteria, the obtained non-uniqueness
of $L^2_tC_x$ weak solutions to the hypo-viscous INS is sharp, and reveals that
$\alpha =1$ is the sharp viscosity threshold for the well-posedness in
$L^2_tC_x$. Furthermore, we prove that the H\"older continuous weak solutions
to the compressible Euler equations may be obtained as a strong vanishing
viscosity limit of a sequence of weak solutions to the hypo-viscous CNS.
