heiress still lives through winter in her Spartan cottage; (line 2)
Here's the beginning of the "not home" feeling we get in the poem. She lives in a modest, spare, austere cottage through winter. Doesn't sound super cozy.
she buys up all the eyesores facing her shore, (lines 10-11)
Those "eyesores" are very likely homes! The heiress buys them all up so she can continue her shut-in, cold-as-ice lifestyle in peace.
there is no money in his work, he'd rather marry. (lines 23-24)
This seems to have an indirect connection to home – kind of like the shopkeeper doesn't want to do what he's doing so much as he'd like to just make a home with somebody.