I'd recommend something in .44 Mag or larger for protection, weight be damned.
Too many people start counting every single gram when backpacking. y general feeling is go with one less shirt, pairof shoes, book, camera, etc. Its worth the slightly extra weight to carry around a weapon that does its job. If you get a hoslter or pack to carry it well, you won't even notice it. I've got a great atachment to my Dana Designs Alpine (pre buyout days) that straps across your chest. It holds a water bottle (ie: Bike bottle) on the outside and has a zippered compartment that is easily accessed and good for maps, granola bars, and the aformentioend .44 mag (Depening on your size and the size of the bag, its big enough to fit up to a full 7inch barrell redhawk)
Pretty sure Dana still markets them. I'll post a picture when I get home.