I was in a situation similar to yours My ex asked if he could move into my house, bought after we divorced, for a few weeks until he found a new apartment. I said yes. Two years later he is still there, doing all sorts of things to make me sicker, or feel that I am sicker. Gaslighting at its finest. He rarely had money for rent or food, and I finally went online and found out how to evict someone in my state. I had a friend serve him with papers that I downloaded and filled out, giving him 20 days to pay or move, and if he did neither, I could serve him with eviction papers. He used me for 2 years, exacerbated my PTSD symptoms, but when he got that piece of paper, he left. I finally set a boundary and he acted. I know you feel responsibility towards him, and don't want to leave when he's sick, but this way gives him 20 days to pack up and leave before you process the eviction.
I feel so much better now that he's gone, and my symptoms are better also. I was so afraid I needed what little money he contributed, but it turned out my electric bill was cut in half and the food bill was a lot less too. It was hard, and made me feel bad, since I hate confrontation and have problems with boundaries, but it was so worth it!
It also might help to write a list of the pros and cons of having him there. Sometimes seeing it there in black and white will help you decide what works best for you. Are you seeing a therapist? Could you work out a plan with him/her? It is easy to say throw him out, but when you have boundary issues and feel responsible (if you do) for someone, it is hard to be cold and do what is necessary.
