5W30 in the cold months and 10W30 in the hot months. Anything heavier then these 2 will burn the valve train up over time.
If it is a k1500, most likely it has the 4L60E transmission.
The 2009 Chevrolet Silverado-3500HD has overhead valves (OHV).
The 2006 Chevrolet Silverado-2500HD has overhead valves (OHV).
The 2005 Chevrolet Silverado-2500HD has overhead valves (OHV).
The 2007 Chevrolet Silverado-3500HD has overhead valves (OHV).
The 2009 Chevrolet Silverado-1500 has overhead valves (OHV).
The 2007 Chevrolet Silverado-1500 has overhead valves (OHV).
The 2007 Chevrolet Silverado-2500HD has overhead valves (OHV).
The 2003 Chevrolet Silverado-1500 has overhead valves (OHV).
The 2009 Chevrolet Silverado-2500HD has overhead valves (OHV).
The 2012 Chevrolet Silverado-1500 has overhead valves (OHV).
The 2008 Chevrolet Silverado-3500HD has overhead valves (OHV).