Should I cover my bicycle overnight while bikepacking? I'm wondering if all the moisture from being out overnight will damage my bicycle. I'm thinking 30+ days of being in use, with maybe a couple of those days being light rain.
If the water will damage my bicycle, are there lightweight and compact covers that could be suggested? Or, would just wiping down the bike with a towel in the morning work to prevent damage?
As Daniel indicates - overnight moisture on a well maintained bike isn't a concern. A little rain won't hurt. Others may disagree but I wouldn't get a cover.  
But, depending on how much rain there is and how long it lasts, when riding in the rain often the rain mixes with dirt/dust/sand and creates an abrasive liquid that can be hard on the drive train - and can even work it's way into bearings and cables.  
Fenders help keep the water mixed with dirt that's on the road off of you and the bike.  
I think of rain / water as a riding factor that increases how often I should do maintenance. 30+ days on the road should include at least drive train cleaning and lubrication.  
Here is a link to an article on bike prep for rain. The article links to washing and lubrication articles.