  We construct the strong weight complex functor (in the sense of Bondarko) for
a stable infinity-category $\underline{C}$ equipped with a bounded weight
structure $w$. Along the way we prove that $\underline{C}$ is determined by the
infinity-categorical heart of $w$. This allows us to compare the K-theory of
$\underline{C}$ and the K-theory of $\underline{Hw}$, the classical heart of
$w$. In particular, we prove that $\operatorname{K}_{n}(\underline{C}) \to
\operatorname{K}_{n}(\underline{Hw})$ are isomorphisms for $n \le 0$.
