This aspect could be difficult to deal with, or it could lend your relationship a feeling of security and stability -- it's all in how you both look at it, and what each of you wants out of the relationship you share. Your partner feels powerfully connected to your past, perhaps to your familial or cultural roots, and they feel a sense of responsibility there. They might feel like they owe something to your family, or that they're somehow responsible for helping to process something that happened a long time ago, something that left its mark on you.
As long as they understand that this is a responsibility they're taking on themselves -- not one that actually belongs to them -- they're able to be of help. They strive to create a safe space for both of you, especially if you two live together. This could come across as a sort of controlling behavior, if you don't understand their wish to protect you. And the truth is, they don't have to take the weight of the world or even of your relationship all on their own shoulders! You should help them to have fun once in a while instead of focusing so much on responsibility and protection. You could feel smothered by all that close, protective attention, but you can remind yourself to try to understand it for what it is -- your lover is offering you the gift of stability in the form of responsibility.