Hey Alex, Welcome to the site.
Have you considered just using a tarp large enough to cover a couple people in sleeping bags? If you plan your trip around good weather a tarp will be plenty shelter. http://www.rei.com/product/808940/kelty-noahs-tarp-12-x-12
I'd think if you are OK with the Bivy idea you would just fine with your bag under a tarp.
If a tarp isn't appealing I'd suggest the bivy route before using a 5+ lb tent.
Try to buy gear you will continue to use if you find bikepacking to be something you would like to continue doing. I bet you would be looking to replace the mentioned tent before your second trip.
Sleeping bags are tough to recommend. This http://www.rei.com/product/778156/rei-halo-40-sleeping-bag
bag can be had had for a little over a hundred till the 24th and would likely do just fine.
What do you have in mind for route? an out and back on the CT?
Curtis in COS