Ugh, I keep trying to resist posting to this thread.
Can't do it anymore.
The average 20" wheel is 35lbs. The stock 16" wheel combination WITH tires is 39.4 lbs. So you're almost as heavy before even mounting tires! I tried looking up tire weights, and realized that no respectable manufacturer makes the size you would need. So you're forced to buy shit tires. Kuhmo doesn't even make the "MX" in a 20" size because no respectable performance driver would be on 20's. But their 712's are available in SUV sizes, and the 255/35/20 is 30lbs. T1-S's also come in that size, but no smaller width. These are essentially SUV tires, they're heavy because they're designed to support a lot of weight. Falken doesn't even make Azenis in a size over 17" because again, no respectable racer (autocrosser) would use wheels larger than that.
The only reason to run large wheels is to run large brakes, and the 3's brakes are completely adequate for track use (when used with track pads) even under 16" wheels.
Anyway, back to weights. You're going to run 35lb wheels with 30lb tires, totally 65lbs compared with 39.4lbs stock. This is not like adding a 200lb subwoofer in the trunk (which is pretty stupid), this is far worse. The thing about wheels is you have to spin them, and that takes much more effort than it does to move an object that isn't spinning. You're dealing with the polar moment of inertia.
I won't bother explaining it since I doubt you care (and Crossbow already touched on it), but here are some numbers for you.
In fact, just for fun I looked up how much straight-line performance you'd lose by switching from 16" wheels to 20" wheels if the wheels weighed the same. It'd be about like adding 200 static weight to the car, which would take an additional 11ft-lbs of torque (roughly 15hp @ the rev limiter) to compensate and get the same acceleration as a stock car. That's bad enough.
But no 20" wheel is as light as the stock 16's. Your combination will weigh 65lbs, remember?
That's like adding nearly 800lbs of static weight to the car. Think about that number. That's almost 30% of your car's entire weight. In order for the car to accelerate like it did STOCK, you'd have to gain back 42ft-lbs of torque over the ENTIRE rev range. At the rev limiter, you'd need to be making 55 extra horsepower. Not gonna happen without forced induction. So basically, you'll need to supercharge your car to keep pace with a stock Mazda3 on 16" wheels.
Bling bling though, right?
Now you know why people with big rims get laughed at. Clowns wear big shoes too, but they're supposed to be funny.
Oh, and that's assuming you get the tires to fit in the first place, and then manage to make it over a pothole. You should aim to keep the volume of air in a tire constant when plus-sizing, which is why you should always upgrade to a wider wheel and wider tire when plus-sizing (a reason why Porsche uses hollow spokes!). Due to fender size constraints, you can do neither, and your brand new $4000 wheels will be bent in no time. The sidewall on 35 profile tires has to be very soft to be compliant, and your car will look like the rims are touching the ground. You know the look- like the tires are low on air. Take a turn and it looks like the rim scrapes, hit a pothole and the rim breaks. Utterly stupid looking.
Oh, and I almost forgot to mention- that extra 800lbs of equivelant weight that you're adding to the vehicle? You're going to have to slow it down, too. Good thing the Mazda3 has awesome brakes, cause you're going to need every ounce of them to stop your car in just routine traffic..
