Well, this post certainly brought a laugh/smile to my face!
I assume that what you have is a large coif or chain shirt? Anything longer than that, like a hauberk, would interfere with your running movement. The amount of exercise that it adds to your run will depend on what it's made of. Steel mail or mail made of thick rings would be heavier, whereas aluminum mail or mail made of thin rings would be lighter. I have a long coif that's made of aluminum rings, and I've worn it for hours at a time. The thing I had to worry about wasn't the weight but the erosion of the metal onto my skin. Aluminum usually looks all clean and shiny, but when you rub it on yourself for a while, your skin turns black, and it takes more than a water rinse to get it off. Of course, if you are
black, then this might not be a concern.
I wouldn't worry about "local sheriffs confiscating your armor" or anything like that. There aren't any laws against wearing armor that's purely defensive. A cop might ask you what you're doing, yes, but arrest you, no.
...and if you have a girl who tells you that they saw you jogging in chain mail and thought that you were a total stud, hang on to her--she's a kepper!