Let X be a smooth rigid-analytic space over C_p. In contrast to algebraic geometry, it turns out that there are many pro-etale Q_p local systems on X that do not admit any Z_p-lattice. Furthermore, cohomology of these local systems often fail to be finite dimensional as Q_p-vector spaces and do not satisfy the naive version of Poincare Duality. At first glance, this may suggest that pro-etale Q_p-local systems (without a Z_p-lattice) are somewhat pathological. However, Kedlaya and Liu observed that these cohomology groups are still finite-dimensional in some precise sense; namely, these cohomology groups admit a natural structure of Banach--Colmez spaces. In my talk, I will discuss that cohomology of pro-etale Q_p-local systems also satisfy a version of Poincare Duality inside the category of Banach--Colmez spaces. Joint work in progress with Shizhang Li, Wieslawa Niziol, and Emanuel Reinecke.