Clear corrugated roofing. Search Lowe's or Home Depot site to get more info. It is lightweight and used for many things-greenhouses, sheds, barns, etc.
Thank you Beverly for your question on this. I too had a custom deck with a pergola but I wish I had some coverage and have thought about a clear roof, like plexiglass. I also want to know how difficult it would be to do myself?
We used the corrugated clear panels on ours. I was not thrilled with the idea, but could find no alternative. I was very surprised how nice it turned out. It only has a slight tilt to it to let the water flow off, so it still looks like a pergola (flat) roof. Very glad we did it = much nicer to have the weather mostly kept off.
The clear corrugated roofing does work quite well for this - and is way more cost effective than plexiglass. Also, plexiglass is not great in many outdoor applications because (I found) it can turn yellow in direct sunlight and become brittle, scratch and splinter in warm/cold/wet/dry weather.
Shade cloth is another option - it isn't water proof and light still filters through, but it cuts down on the heat and glare from direct sunlight.
I used the clear corrugated panels on my deck. It looks good. If I had to do it over, I would use colored panel. In the summer it is very uncomfortable due to the heat. It doesn't provide shade. If you have a shady yard it may not be so hot.
the clear corrugated panels are the best option for what you are wanting. We put one over our deck in the late 80's and never had any problems with it. In fact it was still there when we sold our home in 2004.
I would suggest lexan panels...get the uv protection ones
U can buy phylon or polycarbonate panels with uv protection that are clear. They are usually 2 ft. wide and in various lengths. Use roofing screws used to put metal on roofs to attach the panels. The screws have rubber washers on them so there won't be any leakage.