There are a few expressions concerning bags, and they all seem to be directed at different aspects of life. In my family, we used the expression among us girls (including my mother) about being a bag. So, it became almost like a term of endearment among us that we each were bags. Mama was an old bag, and my sister and I were just bags.
The term about being a bag I think was an old expression that started as a derogatory term directed at an elderly woman who may not have had what we would call “class.” A frumpy, maybe unattractive woman who was not only unappealing, but also had a rather unpleasant disposition. Other expressions meaning the same thing were “old bat,” and “old hag.”
My sister and I had a friend in high school who went with us on church trips, and she would bring more than enough money with her for the trip. We teased her about that, and called her “Money Bags,” which is another expression that contains the word bag. We teased her so much that it because a nickname for her, which was shortened afterwards to “Bags.” For the rest of the time we were close to her, we called her Bags.