We study the relationship between the categories of weak formal schemes and dagger spaces. We introduce the notion of weak formal blowups of weak formal schemes and show that they correspond to rational subdomains of the associated dagger spaces via the generic fiber functor. In analogy with Raynaud’s theorem in formal and rigid geometry, we establish an equivalence of categories between the localized category of quasiparacompact admissible weak formal schemes by weak formal blowups, and the category of quasi-paracompact quasi-separated dagger spaces.