This question might be answered better if it were posted in Living Car Free, even though you're only talking about car light.

If you're grocery shopping once a week, I'd suggest driving the one car one day a week.

You could try baskets, but even the pannier style baskets only carry about one (20 pound) standard paper grocery bag each.

If I were doing grocery shopping for three people, I'd take a pair of my biggest panniers shopping every 2-3 days. The lid on the panniers keeps things from popping out over the rough roads in my city. And the waterproof panniers means things in paper and cardboard containers don't get soggy on the way home on rainy days.