You'll be fine with a four piece (although nothing against a 7pc). It would also depend on the type of pack that your carrying (I would be more prone to a 7pc with an external frame since you already will have stuff hanging off it).
You can't get much lighter than 9/10's of the reels already in production. You figure the wt of the line and backing is standard for the rod wt you will be carrying...so since most reels already weight in at 5oz...if you get what I'm saying.
One big way to cut down on the overall wt is to get an aluminum tube. Take the tube, jam it into some Styrofoam bend it until the foam breaks, then clean the piece up and tape it to the bottom. Take a piece of t shirt and sew a rubber band into it to form a cloth cap. Then use a sock (that you are already bringing) or something to pad the top. You can get aluminum tubes on eBay in most sizes for about 12 dollars shipped. This will make a handful of tubes also. Just don't bring the tube in your carryon. I'm pretty sure its not allowed (the tube part at least).