Seems like this person wants the opposite of what you give this someone.

"At times I'm solitary, yet you want from me;
the person with empty offerings."

^ you are offering your whole attention to her?
and she doesn't not like it??

or she does not like commitment? as it seems she is the sun who gives life to many... so can't settle for one?

so instead of you burning you decide to live that sun and be in solitary confinement.

I think i got it not right, but I enjoyed the read and the metaphors you used. The way you compared this someone, I had to assumed it was about a she.