Sorry to keep chiming in here, but this is a subject somewhat near and dear to me. As I mentioned, I ride a bicycle a lot, used to run, and also walk for fitness, and weight/bulk issues are fairly critical for all of these activities. I've mentioned the carrying methodology I consider best previously, but now to the gun. The 45/410 derringers are pretty big, probably approximating your 642 in weight although might be a little bit less bulky, but it's not an optimal choice. I think that one of the ultra lightweight guns, the 340PD or the 442, one of the J-frames in alloy as opposed to the all-steel 6xx J-frames is your best bet. The Ruger 5-shot revolver, I think it's called the LCR, or the 380 semi-auto LCP would be good choices. So would one of the fine Seecamp semi-autos if you can find/afford one. All are light weight, under a pound loaded. You do need to be pretty vigilant about cleaning and lubricating/rust-proofing your gun, whatever one you choose, because the salty sweat tends to pour when doing these sorts of activities. I've actually contemplated keeping my gun inside of a zip-lock bag, but that's going to slow things down should you ever need it.