Sweat is not always related to not being skinny or not doing exercise. I have the same problem auxren has, I've rusted the polepieces of my JP's bridge pickup. The only way I've found to stop this from happening is to remove the rust using steel wool, and then apply some liquid lacquer over the polepieces (when I did this, I only applied two or three thin coats, because I wasn't sure if it would affect my tone somehow; however, I applied more or less ten coats when I did the next string change, and have never had any issues with rust since then). As to the bridge, I only have rusted the saddle screws of the 6th string's saddle, but there's nothing you can do (or at least that I've found) to prevent rust at the bridge. I also clean the guitar body, neck and strings when I'm done playing.
Hope it helps!