whats the widest tire that will fit on a stock rim for a 2003 chevy cavalier

One, the rim will dictate the width of tire, and the tire also will determine the width that can safely be put on. If you have rims that are 5" wide, you will not get a monster tire that will safely stay on the rim. You need to be concerned with the room you have with a wider tire rubbing on the fender wells when you go over bumps or bottom out at high speeds. If your tire is close to the frame and there is a brake lining bracket, it may slice the sidewall of the tire. When you turn the front tires, will it clear all the steering brackets and fender wells? The tire will tell you the width when placed on a proper rim. Get the tape measure out and find the room you have now, and how much wider you can go on either side. There are spacers to move the rim out some, but if it is hot rodding, you may consider lifting the car a bit. On a front wheel drive it'd really not look too cool. You can get the fender on the front widened and buy larger and wider rims, but how's that look. Tire stores can tell you how large they can go and how wide. My 69 Corvette has 295 X 15 on the rear but I flared the fenders. The front has 265 X 15 and I had to shave the inside rain rims away. I also have 8 1/2" rims instead of 7 " " rims.

Here are the tires and rims after I spent 4 hours cleaning them.