After years of dealing with the shopping bag dilemma, I now think I have the best shopping bags ever! They are made from two recycled plastic drinking bottles. They are extremely lightweight and fold flat when not in use and stand up straight when I need to fill it (I have no bag boys anymore, I must do it myself). They hold as much as a paper bag and are even stronger for those days when the bottles of olive oil go on sale. They are convenient and all the same size.
You see, I buy them at my grocery store here in Europe. The bags can be purchased for the equivalent of $2 at the checkout stand if you have forgotten to bring yours that day. They hang right beside a stack of paper sacks that can also be purchased for 30 cents each, instead. You just put them up front on the conveyor belt with all of your groceries and the clerk rings those up first and you are ready to load (in Europe, you are packing your own; I am not sure about the US). The small, very thin plastic bags are only supplied in the fruit and vegetable area and the checkout clerk has a roll that she will use for certain items that she thinks might need extra security, such as containers of berries. You can also ask her to give you one for something you might think needs extra security, such as raw chicken. What I mean to say is, that while there is single-use plastic, it is just used very little.
Europe, like the U.S., is also always evolving on the environmental front. When I first moved here the reusable bags that I purchased were made of thick plastic or waffle weave plastic that was very strong, and stood on its own for loading, but it had a fault too. These things would not fold flat for storage, they loved to stay in their open, crinkly shape, and took up prime closet and trunk space. They have certainly improved since those days.