Hi Teddy , do you think that having a "heart to heart" talk with this/any someone about the way you're feeling might help. Afterall it might be your perception/fears that they're finding you/might find you a burden, rather than the way they actually feel about you.
And you know, if you're right in the feeling that they might want a bit more of their own space, then at least you're giving them that opportunity to give you some feedback on what they'd prefer you to be doing/not doing to keep the relationship strong.
Then of course you'd have some guidelines to work to, and know that while you're sticking to them the other person is happier in the relationship, and hopefully be a bit happier yourself knowing that.
Attachment/abandonment issues can often link in with BPD though, so you're not alone!!
And while sometimes what you might really want from the other person is reassurance/to know that things are "alright", maybe you could work on finding some more of that reassurance inside you??? And perhaps working on a bit of "self monitoring" as well e.g. have I really done/am I really about to do something that might push that person a little further away or not??
And you know maybe a little work on your self-esteem/confidence???
Just some thoughts.
I do know that "technically" it can sound simple put like that, but it really it can be far from that.......but it's great that you're recognising it as a problem for yourself and that you're talking about it, wanting to resolve it........certainly a "step in the right direction". And good on you for looking for support with it!!!

Alison