Your sheer curtain bag sounds like a good idea. The fabric should have minimal weight, as that would add to the cost of the produce. When I make what we call "bird curtains," or seed catchers, from sheer fabric, they need a French seam. They usually hold up to the canaries picking at them, but they are not holding any weight.
Here is one examle of a produce bag that Reusable bags sells. http://www.reusablebags.com/store/organic-cotton-produce-sacks-p-747.html With the draw string bag, it wouldn't be much of a problem to open it up for the cashier to look inside. I wonder how much weight the bag would add to the produce?
We have an eclectic mix of reusable grocery bags. I use them frequently, as most of my grocery shopping is at Alidi's, Save A Lot, and BJ's. Stand alone bags are my preference, although we have only a couple of them. When my daughter and family were in Helsinki last winter, they found that stand alone bags were what most people used after covered trolleys.
To cut down on produce cost, and for my family, waste, the only produce I buy are onions, garlic, carrots, potatoes, apples, and sometimes fruit in season. (By using frozen veggies, along with the produce I do buy, the cost is offset by the reduced waste.) Currently, I have been buying onions at BJ's which have a very nice mesh bag that could be reused. Maybe a reusable onion bag might work as well.