WishDesignStudio from WishDesignStudio says
Maybe some small drinking glasses/tumblers behind them and use a bit of double-sided tape to hold them up? Actually, a piece of folded cardboard and some tape would probably do the trick.
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While I don't have any paper weight I do own a lot of glasses, so I like this idea. I have one shot glass which seems like the right size to stay out of sight in the photos. To make it heavy enough to support the bag I was going to fill it with change.
That go me thinking about other things that are about the same height. I found the following items to be about the right size and weight: A can of anchovies, a can of sardines, and a box of staples. Of these the stapes seem like the best thing for my situation. I'm going to cover the box (which is bright red) in white paper so it is less noticeable when it shows up in photos, and easier to Photoshop out.
Last night when I was photographing my bag I did have problems with the bags slipping. I took some white poster putty, rolled it out thin, and then stuck it to the paper. It kept the bags from slipping. Then I put the bag handle over it so it would not show up in the photos.
I think a strip of double sided tape might work well too to keep the bags from slipping, but I don't have any. If I did I would try it and compare the two.
I appreciate all the suggestions that were made, and encourage people to keep making them, or to talk about things that work for you. I think other people will find this thread useful.