The cloth bag is too small

Too small? Get a bigger cloth bag then. Or is there just one size of bag in LA? I have several cloth bags that carry more than a plastic bag, and I don't have to worry about too much weight breaking them or double bagging.

making them requires a lot more fuel & water than a paper or plastic bag, and washing them wastes fuel & water too.

Well, since cloth bags predate the use of fossil fuels, I'll go out on a limb and say that they don't need use that much fuel, and they also can be made from old cloth in recycling efforts. Washing them doesn't come up much either; you don't have to wear them, just carry them. The fashion sense concern is pretty minimal (perhaps a skewed LA perspective?). Hardly anyone who would carry a fashionable bag like you described (teenage girls, one would expect) would actually be carrying groceries very often.

And to really cut down on the bags, get a backpack, and carry the heavy stuff on your back (20-30 lbs on the back is a hell of a lot easier than in your hand).

If you're carrying fresh meats and vegetables home in a cloth bag, it had better be clean. If each meat or vegetable you put in the cloth bag already has its own plastic bag, or each dried good you put in the cloth bag already has its own cardboard box, then how are you saving the environment with the cloth bag?

Of course, if these products are all made by enormously fossil fuel subsidized processes to begin with, then the cloth bag is just a convenient way to enjoy the benefits of fossil fuels without feeling guilt for destroying the natural world. :)