My H does the same as your W and it serves 2 purposes:
1. She's hinting that she still finds you attractive and in an indirect way she is investing in your R.
2. She is trying to control you because if she's single and not looking for another partner, she will hope you will follow suit and take example by her behaviour.
If you know there are no other men, you hold onto hope and don't get any other women, don't move on with your life etc.
It is a way of keeping you near to her and ensuring you don't fall in love with somebody else, esp. the offer to hang out in her house.
She wants to own you without the commitment. I think you did well to say no.
