This seems obvious to me why the heavier bags are better. They don't immediately blow away to the ocean or wherever else. We're also charged $1.50 for them where I am or you get a paper bag so people who want to save $4.50+ on a grocery run (which is a ton of people) will bring their own.
The problem with that is, in places where delivery is ubiquitous, people use the reusable bags the same as they used the single-use bags, and there's no way to return them, so now people are disposing of much more resource-intensive bags the same way they did the single-use ones.
Those same people who will save $4.50 by using the reusable bags also wouldn't think of paying for delivery. And the reusable bags are much more likely to be recycled or used for other purposes.
But also where I am people deliver 100% in boxes. That's an easy enough way to solve it. Also makes the delivery of a heavy load easier because you just drop the box on a dolly or similar.