So I am dating this person and they have BPD (Recently diagnosed) and although they took it pretty bad at first, they're a lot more accepting of it now. I love them a lot and I know they love me a lot. 

They are a lot more introverted than I am and as a result they like hanging out at home a lot more than I would. Usually this would be fine, but 95% of the time they hang out at home, they would just be really sad and convince themselves that the only reason they are at home is because no one invited them to go out. A lot of the times that this happens, I also choose to change my plans and spend time with them at home, but that has started affecting my mental health negatively.

Now I don't know what to do because if they stay at home alone and I go out, I can't have fun knowing they are not having fun at home. But if I change my plans and spend time with them, that's affecting me negatively too. Either way something bad is happening and I don't know what to do :(

Any advice will be greatly appreciated...