For the speaker, rain isn't gloomy weather. It's a relief. Each time it falls, something inside them settles, and the storm outside seems to quiet a restlessness they carry around all the time. They describe standing out in it for hours, soaked and chilled to the core, and instead of misery they find calm.
The feelings in the poem are mixed. The speaker says the rain leaves them "boneless and aching" and "wanting in a way I can't put into words," so the peace isn't simple happiness. It feels more like exhaustion mixed with longing, a release that still leaves something unfilled. The image of the storm wrapping around the ribs and settling near the heart makes the weather feel like part of the body.
By the last line, the storm outside and the storm within have become one. The mood is quiet, intimate and a little wistful, like someone finally being understood by the sky.