The relationship between wheel mass and strength has already been mentioned, but there is also another relationship that is usually there: heavier wheels generally feature wider rim widths.
Rim width affects the performance characteristics of whatever tires that are mounted, four that come to mind are:
1) Tire profile. As rim width is increased, most tires will become more square-shouldered. This affects many things, including rolling resistance and the way that they corner.
2) Tire contact patch. As rim width is increased, tire contact patches will get bigger, which changes rolling resistance but generally increases traction. The changes to rolling resistance may be brought about by the combination of additional tread contact/squirm (increases rolling resistance) and increased flotation (decreases rolling resistance).
3) Tire carcass stability. As rim width is increased, the tire carcass becomes more resistant to sideward deflection, which in combination with momentum/gyroscopic effects, makes the bike much more stable in side impacts, ie rock gardens.
4) Tire volume. As rim width is increased, the tire volume is increased. This allows you to run somewhat lower pressures without increasing the risk of pinch-flatting.