At each corner I've run braces from the roof 2"x6"s to the upright corner 4"x4"s.
Here's an inside view...
The base of the screen house is lag bolted to the deck, so I can't see heavy wind lifting it up. But perhaps it could torque, so I will be adding corners braces to the bottom too.
If anything would happen during a heavy wind, I figure it would be the plastic roof coming off. After all, it's just plastic. But I don't foresee that happening for a number of years because the plastic is new. Once it gets old and brittle, all bets are off.