To add to comments from leisa and white knight
Family is important.
Being involved and assisting in essential activities such as shopping can feel like an obligation you're pulled into, in this case you're not wrong to feel the way you do, and there is nothing wrong in feeling that.
Help your family where you can
Balance is important.
You are an individual and they need to recognize that as well. A good down to earth conversation with your family is probably worth while
Plan in advance,
Plan for the weekend you want and then where you're free add family in a way where you can help or even just maintaining some communication.
Plan for the weekend you want and make sure to build habits and routines that work for you, that benefit you, to consider the fact you've come to this forum you obviously feel like you're being held back enough that you're losing the connection to the outside you would so definitely enjoy.
Maybe organise to do a shop at the end of a normal week day to get most if not all required items freeing up the weekend
I've spent a lot of my time not doing what I want because I've really put my effort into avoiding my family and even going out and being active may generate conversation which means I then may be at risk (in my head) of being criticised for something.
I've broken my habits and connection to nature by not being involved in it for whatever reason, only now that I live out of home and I have time for myself am I finally going to the gym, going on walks, doing gardening, sitting in the sun with my cat etc etc etc.
Your family should understand if you can't help EVERY week
Deffinetly help some weeks but find the balance.
All the best my friend.