If the overall diameter of the tire tread is different, that's just like changing gear ratios. Smaller diameter is like having a shorter final drive ratio (larger number, like a slightly lower gear).

If you choose a larger wheel with a lower-profile tire, you can maintain the same overall tread diameter. Then you can worry about weight. Even if the new ones are about the same weight, that weight might be concentrated more towards the outside of the tire. Then it has more rotational inertia, which kinda acts like MORE weight. Every pound you add at the tread is 'worth' 2 pounds on the car. Every pound at the hub is only worth the one pound. So each pound you add to the tire/wheel is worth somewhere between 1 & 2 pounds.

Often the larger wheel & wider tire will give better cornering, this might be more important than the weight. Sometimes the looks is even more important than the performance...