Dweb protocols, like DAT and IPFS, promise significant benefits over the standard client-server protocols for web content. Particularly for self-hosting and -publishing, these protocols could reduce barriers to entry by eliminating server costs as well as promoting data ownership. Despite this, there has been no adoption of these protocols in mainstream browsers yet. This talk gives an overview of work to add native-like support for the DAT protocol to Gecko-based browsers. We discuss the limitations of the current WebExtension APIs in Chrome and Firefox for this purpose, and how Firefox's libdweb project improves on this. We present the dat-webext browser extension which implements DAT support in Firefox on Desktop and for Geckoview on Android.