I replaced the back tires on the tractor a year ago, and kept one of them to use to flip. It works fine. It is a 26 inch tire. I don't know how much it weighs, but I can flip it about 15 times in a row. It is a real good aerobic/all around workout.
As far as adding weight to a tire, I don't think you can do that. You might just have to trade it in and get a larger one. Most places will give them away, just to get rid of them. The only hard part is getting the SOB home. My suggestion is go someplace that has some tires, and try flipping them. Get one you can just barely get up, and use it for a while. I have some 12.00 x 20's here at work I would just love to give someone. They would probably work great for a woman. They are too light for me.