The recommended weight of motor oil for a 2003 Chevy Silverado 2500HD with a 6.0L gas engine depends on the climate where you live and the specific recommendations in your owner's manual. However,
5W-30 is a very common and likely appropriate choice for most situations.
Crucially: Always check your owner's manual. The manual will specify the recommended oil weight and viscosity based on temperature ranges and operating conditions. Using the incorrect weight can damage your engine.