How can I make a lightweight structure (sukkah) stronger and more windproof?
You have two separate issues. #1 is keeping the wind from taking it... because if the wind lifts it off the ground, it will get wrecked. This type of structure is not made to survive being a tumbleweed.
So tying it down is non-negotiable. I'm partial to spiral (corkscrew) ground anchors, because they let you use all the ground above them as your virtual sandbag.  You want to fantastically over-do this job.  Very consistently, people underestimate the wind and their tent stakes pull out. Nobody ever said &quot;Wow, these tent stakes are stronger than we needed&quot; :)
Part of staking is guying - that is, come from the top of the structure diagonally (looking from the side, not the top) to a tie point on the ground. There can be up to 8 guys of this sort.  One might be tempted to have four guys diagonally (looking from the top also. That would create interesting forces in the walls. Guying, on the sides you are able to guy, helps the structure resist tramming (shearing/parallelograming).
What will also help that is internal bracing, or better, rigid sides.  Bracing can be done by making an &quot;X&quot; with tent ropes which you then cinch up taut.  However, bracing will increase the compressive load on all elements of the structure.  So this might just mean the wind bends the structure all up.
So the better plan is to rigidize the structure sides with something like plywood. Assuming that's ... kosher?

Given the canvas exterior I would probably add a face on the inside of two opposite (non-door) walls... full width and height and notched to clear structural members where needed and let the velcro be used.   Tie that to the existing structure however as suitable, drill and screw, or use conduit clamps.
Then I'd measure the distance between the two faces on the inside, and make a third face that will go full width - no need to tie this one to the structure because it'll tie to the other two walls with angle straps.
At that point you have 3 sides that are very rigid and will strongly resist tramming horizontally. And better, it will not be transferring high forces onto the metal structure the way cross-bracing ropes would.
It would be nice to have a fourth side to resist twisting... but I gather you need a doorway.

The last issue you'll have with tramming is &quot;from the sky looking down&quot;.  For that you need cross bracing in the horizontal plane.  Doing a good job of staking the structure will probably take care of that. But you could also do an &quot;X&quot; under the floor, or better, as the floor!  Again, tied to the 3 walls with angle straps.  That structure isn't going anywhere!