I am with Russell on this one...attach your "printed sheet backdrop" to a piece of Masonite or similar hardboard that you can work with at your desk or work table. Attach by setting bottom on benchwork of layout and simply using small brads along the top that help keep the Masonite from sagging over the years.
If the backdrop runs along the center of a table/island style layout section you will have a couple of options that work well enough...
First, you can (during construction, but it sounds like you are past that phase) attach the backdrop to sturdy framing below the top of the layout...in other words, build "around" the backdrop rather than add it later.
Second, if you already have the layout in place and you are retro-fitting to a "table top", if possible, "cut a slit" in the center of the table top that you can slide the Masonite in, attach bracing below the table top then remove Masonite and attach backdrop.
Third, "IF" you can "hide" it, attach a small piece of wood on top of the layout and screw the Masonite to that. I used this approach on one HO layout. The "base" I used was whatever scraps I had (2x4 in a couple of places, 1x4 and 1x2 in others) as one side was going to be covered by a hillside, allowing me to completely hide the base on that side. How did I hide the screws? Well, where possible, I placed "puff ball trees/shurbs" and structures, etc. It lasted several years without any hint of "sag" before I had to take down the entire railroad. I used the same technique on my next layout...however, I elected to use smaller wood pieces.
Another option for a shelf layout is to screw a base along the back and affix the backdrop to the front of the base.
Using the above option on a table top/island, you could use "twice as much Masonite" by simply putting the "screw base" along the center and putting Masonite sheets on both sides. You can put a small piece of the base material on the visible ends and painting "sky" color.
Finally...and this is worthy of notice...
A friend elected to use sheet vinyl flooring in the corners to permit a smoother curved corner. Where the vinyl meets the Masonite or other backdrop, you can smooth the joint with spackling.