How about a bungee cord running underneath the chair or table, hooked into the bottoms of the covers on either side?

Good idea, but does this mean I have to make holes in the covers to hook the bungee cords? I'm afraid if I make holes the covers will rip with a strong wind. I'm willing to try it because I've ran out of ideas. Thanks.

use 2 or more bungee cords and go around the entire piece of furniture.

Oh, now I got it!!!! Yes, I think that will work. Thanks.

Or you can put grommets in the holes so they won't rip.

I didn't use the bungee cords, but I used a nylon rope and tied it all around and so far, so good. I'm waiting for a strong wind to see if it stays, but I can't imagine those covers blowing away. I'm very thankful for your ideas, because I've spent many hours putting those covers back up every time we had a light wind. Thank you so much.