Owari Nochi, Asanagi Kurashi.

Seven Seas describes the story:
A young girl named Nagi and a giant spider make an unusual pair in this post-apocalyptic story, but living in the mountains is lonely, and they've managed to find each other. Join them in their strangely sweet domestic bliss as they spend their days sharing tea and throwing picnics, proving that love (and delicious food) can bring together even the most unlikely of friends.