My interpretation is the person she is singing about was burned/hurt by a previous lover, and now the way he treats her makes her realize that they both share that in common now - he was burned by another lover and now he passes that hurt onto her and now she also feels that burn, because he is the one that's hurting her, just like his previous lover hurt him.
The end line sums it all up
"Just don't come home and say
You've been asleep
When you know you're burning
Someone.
That common burn"
She's saying: Don't pretend to 'be asleep' when he should know better from his past experience of feeling burned by someone and now he's burning her and now they also share that feeling of being burned.
My interpretation is the person she is singing about was burned/hurt by a previous lover, and now the way he treats her makes her realize that they both share that in common now - he was burned by another lover and now he passes that hurt onto her and now she also feels that burn, because he is the one that's hurting her, just like his previous lover hurt him.
The end line sums it all up "Just don't come home and say You've been asleep When you know you're burning Someone. That common burn"
She's saying: Don't pretend to 'be asleep' when he should know better from his past experience of feeling burned by someone and now he's burning her and now they also share that feeling of being burned.