In this paper we are interested in finding and evaluating cardinal characteristics of the continuum that appear in large-scale topology, usually as the smallest weights of coarse structures that belong to certain classes (indiscrete, inseparated, large) of finitary or locally finite coarse structures on $ω$. Besides well-known cardinals $\mathfrak b,\mathfrak d,\mathfrak c$ we shall encounter two new cardinals $\mathsf Δ$ and $\mathsf Σ$, defined as the smallest weight of a finitary coarse structure on $ω$ which contains no discrete subspaces and no asymptotically separated sets, respectively. We prove that $\max\{\mathfrak b,\mathfrak s,\mathrm{cov}(\mathcal N)\}\le\mathsf Δ\le\mathsf Σ\le\mathrm{non}(\mathcal M)$, but we do not know if the cardinals $\mathsf Δ,\mathsf Σ,\mathrm{non}(\mathcal M)$ can be separated in suitable models of ZFC.