I took my bear cannister on a couple of trips because I figured even if I wasn't worried about bears, it would make a decent camp stool and keep other critters out of my food. I never found a campsite that didn't have a bench or picnic table. I don't carry it anymore.
I did, however, recently pick up a couple of Pocket Chairs (
http://www.amazon.com/Allstar-Produc.../dp/B004P33I70), and, while they don't actually fit in my pocket, they easily slip into a pannier. Possibly not much lighter than your chair. Not great, but better than nothing when nothing is what you have, although, as I said, I have had good luck in finding seating when camping. However I've never done the GAP & C&O.
There is a temptation to put this in my bag on my next trip, but there is also a lot to be said for leaving behind items that, at best, might only have occasional use, especially when they add significant weight and volume.
Only you can decide whether how much you're willing to put up with to have an assurance of a seat. I waver. My hammock tent can double as a chair, though, so it may suffice. Can't really pull up a hammock around the campfire though. Someone else can speak to finding seating on your route, but you will have to decide how much not sitting on the ground is worth. My thinking is that it's not worth the trouble, but that doesn't mean I won't make the opposite choice when I pack up.
Here's one that might not break the bank and looks to be half as light as yours:
http://www.jacksrbetter.com/shop/camp-stool/