You don't have to change tire sizes, just go up in the load range..
You can get Load range E in your default size of 205/75 R15..
SEE HERE"Capacity: Load range: E Ply rating: 10 Maximum load: 2,830 lbs at 80 psi Maximum speed: 81 mph (speed rating M) "2,830 lbs capacity and plyrating of 10 which is the same as 225/75 R15 Load range E.
Going to 225/75 R15 will net you nothing than paying more and perhaps due to larger diameter might even scrape/rub the wheel well and at worst wheels may end up touching while in motion..
Moving up to Load range E will also require airing up the tires to maximum side wall pressure of 80PSI get that extra capacity. Airing LR E to 50 PSI may net you LESS capacity than a LR C aired to 50 PSI.
This may exceed your max rim pressure if you have LR C tires (LR C side wall pressure is 50 PSI).
Honestly, since you just bought it and if it is brand new off the lot, I would recommend using as is. For the most part, unless you are severely overloading and or underinflating the tires spec'd by the manufacture will meet the absolute min of required ratings.
The main key here is to make sure you inflate and maintain the tires to the SIDE WALL PRESSURE. Generally as long as you do that they should be fine..
After the tires have worn down then consider moving up to a heavier load range, IF you experience a blown tire.. Higher load range adds weight which can be problematic with braking..