Hi everyone,
Exhaust is something that is talked about heavily in my area of the car world (that being the Datsun 510 where almost everything is custom made). 1 7/8's sounds about right for stock exhaust. Look at big power house cars like my buddies Acura TL-S (350hp if I remember correctly) and you will see the pipe size if WAY smaller than one might think. This is to keep low end torque strong. Increasing pipe size will lower low end torque but free up flow giving you high end hp increase. It's not a huge change but it is a change.
Also, theoretically, if the exhaust was 2.5 inches and the tip was 2.0 you could launch a tennis ball out farther than a 2.0 inch system all the way back!

The area behind the blockage is what would determine the amount of pressure built. The larger diameter behind the tennis ball would allow a greater volume of air to compress and consequently a greater volume of air wanting to escape. Think of it as add more gun powder behind a cannon ball. My dad used to tell me stories about when he was a kid and would stuff tomatoes and potatoes in peoples tail pipes in parking lots and watch them start their car up. The cars would stumble and they would rev it up and the fruits and veggies went flying!
That 2005 Mazda3 came with two different OE systems, split system and a single piece system, You could buy the factory tip from the split system and have it welded on. The piece isn't cheap though. Dealer list is 111.44, dealer cost is 66.85. I sell it to forum members at 76.88 plus shipping.
ALSO! The OE split system DOES use clamps like a muffler shop as indicated in the picture below which came from our factory catalog. The main difference is the aftermarket kits, like from napa, save on price by not adding things like a nice expensive tip.
Hope this helps,
Chris
Autotown Mazda