Do you just need to write markdown? Plenty of text editors have a vim mode. Not sure if there's any lightweight ones that do the markdown preview alongside a vim mode; I know IntelliJ-based IDEs have a vim mode and can preview markdown, but that's not exactly a lightweight solution, and only the community edition is open source.
But also what exactly is it you're looking for that Vim can't do? I use Vim for writing pretty much everything. I use Vim for markdown and it works fine. Markdown is already pretty readable as a text file so I don't feel the need for a previewer or anything like a rich text editor (but also there are plenty of markdown editors out there if you just want to edit markdown in a RTE).