Does anyone have any insight as to the meaning of this poem?

I think the poet is using the tree as a metaphor for her own emotional state. I believe that is the meaning of the phrase "window tree" in the first line, i.e. she sees the tree as a tangible manifestation of her inner state. The girl is in love and she pictures her love to be like the tree outside the window. It gives her a "vague dream-head", ungrounds her, and fills her soul with light, which I believe she is talking about in the second stanza as being "the thing next most diffuse to cloud". I think "light tongues" refers to the way sunlight plays on the leaves of a tree and is also a play on the sound of the leaves themselves. I think she is referring to in the third stanza as creating a storm in her the way she sees the tree tossed during a storm. The last stanza refers to inner weather, because the girl is preoccupied with her emotional state, which is love. Thus, we now understand the meaning of the first stanza - she never wants a curtain drawn between them because she never wants to lose the feeling of being in love.