I have had one of those Veranda (Classic Accessories) covers that HD sells for a year now. It is quite a bit heavier and cheaper (price-wise) than the Weber cover. I have not noticed any "sweating", at least from what I can see. However, I grilled on Monday night and a *&^%$!!!! thunderstorm came in, before I could put the cover back on, with golf-ball sized hail and completely soaked the bleeding BBQ, now the lighter won't work (will have to try drying it out, if not take it apart and clean it).
The Veranda cover I got was the medium. A little big on the Spirit, at least the 2009-2012 model, but it's supposed the fit the Genesis like a glove. On an aside, I bought another Veranda cover for my 22.5 OTG and that does fit like a glove.
edit: Ah, I now noticed you specified another BLACK cover. The Veranda is a weird yellowish-beigy sort of colour. However, no one will know that you have a nice Weber BBQ under it.