High oil consumption 2001silverado 4wd, 4 door 6.0

How many miles on your vehicle ? Do you see any leak spots on the ground from the truck ? Blue exhaust , oil burning , valve guide seals , piston rings , PCV clogged .

Oil Consumption Diagnosis
Checks
Causes
Excessive oil consumption, not due to leaks, is the use of 1 L (1 qt) or more of engine oil within 3 200 kilometers (2,000 miles).
Preliminary
The causes of excessive oil consumption may include the following conditions:
• External oil leaks
Refer to Oil Leak Diagnosis .
• Incorrect oil level or improper reading of the oil level indicator
With the vehicle on a level surface, run the engine for a few minutes, allow adequate drain down time, 2-3 minutes, and measure for the correct engine oil level.
• Improper oil viscosity
Refer to the vehicle owners manual and use the recommended SAE grade and viscosity for the prevailing temperatures.
• Continuous high speed driving and/or severe usage
• Crankcase ventilation system restrictions or malfunctioning components
Refer to Crankcase Ventilation System Inspection/Diagnosis .
• Worn valve guides and/or valve stems
• Worn or improperly installed valve stem oil seals
Refer to Spark Plug Inspection .
• Piston rings broken, worn, or not seated properly
Allow adequate time for the rings to seat.
Replace worn piston rings, as necessary.
Refer to Cylinder Leakage Test .
• Piston and rings improperly installed or not fitted to the cylinder bore
Refer to Lower Engine Noise, Regardless of Engine Speed

Sounds like the cats had its day here and needs changing

have an accredited service shop to a wet and dry compression test on the engine
That determines engine condition
have the oil pressure checked using a mechanical gauge and if the pressure is below specs that indicates worn bearings overloading the oil control rings
leaks can be rear main seal or crank shaft seal at the front where the oil is blown away in the slip stream

go t auto zone and have them run a diagnostic for free when the light is on , that will tell you the problem easy , or you can buy an OBD scanner,

No oil on the stick does not mean the engine is dry.Usually only about two quarts show on the stick.Top it off and look for leaks.Some oil consumption is normal on break-in.1000 miles should seat the rings so if you are still missing oil after that whoever rebuilt needs to take a look.Good Luck!

Because your car is consuming so much oil, you need to check the level often, so the level won't go down more than one quart. You will get an idea how long you can drive the car before it is down one quart, and should keep the level at the full mark. You should change the oil filter, as it is still collecting contaminants.
Have you checked the spark plugs condition? It seems the oil consumption will result in the plugs being fouled soon . Keep that oil level up, or the result will be a seized engine. Also, I'm guessing the tail pipe shows black residue, another sign of high oil consumption. This is probably why someone sold this car, they didn't want to deal with an expensive repair of an engine rebuild. You are correct, an oil change should be done every 3k miles.

service it like you would the truck engine it will have to be reset by the book almost like the truck i had that same problem

Your check oil light correct? if oil level is full then you have a bad oil level sensor

Look for Castrol TWS 10W60 Motor Oil. This car should not burn so much oil, you need to use a different kind. It is recommended by BMW as well. I also heard the VANOS isnt an issue anymore, can be fixed with a different MAFF. Good luck!

The oil you took out was probably a lighter weight. A heavier oil will show a higher oil pressure. Make sure you are using the proper weight for the temperature conditions in your part of the country.
Squido