Every other day for me.
My parents went to two different grocery stores when I was young. They had one grocery store that they went to once per week to replenish storable staples. Then there was another smaller store closer to home that they went to maybe twice per week for fresh stuff.
If you want "convenience," you can stock up on processed foods and shop less often. You'll save time and gas, but your health will suffer. IMHO, it's not worth it. As my grandma used to say, "If you don't have your health, you don't have anything."
I am like your parents and do a stock up trip at the big grocery store on weekends and stop at the small IGA that’s on my way home from work for fresh items.
Does anybody else live alone? My problem is waste. I get sick of the food before I eat all of it, or it spoils before I can get to it. I sold my big freezer last year because I didn’t keep enough in it to justify the electricity it took to run it. I eat almost all of my meals at home. Work is close by so I even run home for lunch and brown-bag breakfast. I do consulting work afterhours and on weekends so like to keep something here to save time. Sometimes I think it might be cheaper for me to do take out.
I do that. I have a local market, right down the street, with an excellent butcher. Go there every other day or so, for food for a few dinners, keep up with the milk and lettuce. Every few weeks I go to the supermarket not too much farther away, get larger amounts of staples, paper goods and so forth.