I agree. Tarps are not a good idea.
Also, I have been using Gas Grill Covers. Not that I have or ever will own a gas grill (blasphemy in my parts).
They are breathable but keep the moisture out and come in a very wide range of sizes and shapes. I started using them by chance and have continued to use them since. Mostly on my bikes, but I have used a large on a Kart.
The good ones are expensive, but I've noticed they ain't really big sellers. The trick is to get them during the right before the grilling offseason (which doesn't exist around here). Most big box stores put them on clearance.
Last year I bought two really big & nice ones from Sam's Club on clearance for $9 each, regular price was around $50 each.