I've never lived in a dense city so I don't know how this is done.
I doubt I could carry a week of groceries for my modest family (2 adults, 2 children) 1 block, let alone several. Do you maybe use personal carts or what?
Family of 3, our supermarket was in the groundfloor of our apartment so it was sometimes easier to just run downstairs and grab it then to search through the pantry. You'd be amazed what you can carry once you start doing it regularly. I also, proudly, walked around with those little carts you see little old ladies carry. Damn things are super useful even with a car. Carries 2 cases of beer and produce on top ;-)
The other grocer in our neighbordhood does deliveries. Go shopping as you normally do, at checkout groceries are loaded into a big plastic tote instead of a grocery bag. It's delivered to your door within the hour.
I grew up outside the cities (denser, working class suburbs, not mcmansion-style suburbs) and after city living most of my adult life I can't realistically go back.
Short answer, you don't make weekly trips because the grocery store is down the street. I walked by two good grocery stores on my way home from the subway when I lived in NYC, I'd just buy what I needed for that night.
Or you buy your own cart, you see them all over in NYC, for groceries and laundry.
Father of family of three here who regularly walks; I use a large backpack and a pair of large reusable bags that I throw over each shoulder. Heavy stuff (milk, canned goods, bags of apples, etc.) go in the backpack.
Invariably, I forget something so I usually have a smaller midweek trip for things I forgot. The walk to Trader Joe's is about 20min each way.
It's a different perspective if you've never had to do it; I used to live across the street from a small grocery (Fresh & Easy). When the grocery store is across the street, you don't bother with a week's worth of groceries.
You just run over to get some things for dinner or for a couple of days. You can fit a surprising amount of food in a single grocery bag.
When the grocery store is just five minutes away on foot, you don't have to shop for the whole week. It essentially acts as an extension of your cupboard/fridge/pantry.
And long lines at the grocery store are an artifact of the city.
The walk to my grocery store is under 5 minutes. I shop every other day because I can shop before 7AM. But if I had to shop later than 7AM, I would only go once a week, because the lines grow too long.
It's also the case (though less true of families) that a lot of New Yorkers basically don't cook. Kitchens are generally tiny and there are a ton of restaurant/takeout options. (Plus lots of activities that many would prefer to spend their time doing rather than cooking.)
I've never lived in a dense city so I don't know how this is done.
I doubt I could carry a week of groceries for my modest family (2 adults, 2 children) 1 block, let alone several. Do you maybe use personal carts or what?