Those thoughts are just your feelings trying to bring their concerns to light. If someone you cared about came to you feeling this way, would you join in on their concerns, stirring the pot with what-ifs and all that? Or would you want to reassure them? Support them? Give them advice?
What if you gave support to those feelings you experience, not in a way that gives them credence, but treating them like someone vulnerable that doesn’t have the ability to reason that much for themselves? Like a young child or a pet. They don’t necessarily know that there’s nothing to worry about, they just react to things that scare them. Your feelings are the same way.
If you trust these people, being open to them may be another way to start that dialogue, but that can be a bit tough. I do recommend trying to start that kind of dialogue with yourself. You can first ask yourself, what’s so bad about being a “burden” to other people? Would the things you do be a burden to you if it came from someone else? Can you trust these friends to let you in the way you’ve let them in?