When you install wider tires without changing anything else, the size of the tire’s contact patch (i.e., the rubber touching asphalt) stays relatively constant. That size is based on a tire’s overall diameter, inflation pressure, and the weight acting on it. Installing fatter tires widens the patch, but it also shortens it front-to-back. Because of this, cornering gains can be offset by diminished straight-line traction, including braking and hydroplaning resistance. The increased mass and friction can also translate to slower lap times and a drop in fuel economy.
If you want to improve cornering grip, you’re better off switching to a higher-performance tire of the same size. Buy right, and you’ll get a stiffer sidewall for crisper turn-in and steering feel, as well as a stickier rubber compound and a tread pattern focused on dry grip.
Width won’t do it. Merely increasing the width of a tire doesn’t increase the area touching the pavement. It just makes it a wider, shorter patch.
A bigger donut. If other vehicular factors remain constant, increasing a tire’s overall circumference is the only way to enlarge the contact patch. Of course, your car’s body and suspension were designed around a specific tire circumference. Changing it might cause more problems than it solves.
Pressure and weight. Reducing air pressure or increasing the weight on a tire increases the size of the contact patch. But again, there are drawbacks. Some poor engineer has already fought this battle: Keep the stock size and just buy a more aggressive tire.