Sumatra is one of the (few) win apps I miss since recently converting to linux. Running it under wine seems like overkill, but I wish for a debian port...
Sumatra makes heavy use of the win32 API so a port is not possible. This design is why it's so good (light, fast, well integrated) and the author refused to lessen his software by using a cross platform framework.
I will put up with less functions for the better feel.
However many people want to appeal to more users or program in Linux or web and so have a default cross platform GUI anyway (or make it cross platform easily)
If you want something still more lightweight, Zathura would be the way to go. It can be a tad too minimalistic, but great for LaTeX with vimtex, and for an occasional quick document, the startup times are phenomenal.
But one thing I really hate with it is that if you rename a file while it's open, it'll stop displaying it. Not sure if this is related to zathura itself or to the backend I'm using (mupdf).