This brochure may help you:
http://brochures.slosh.com/pdfs/1986...Trailering.pdf
I agree on 6-7000lbs likely not being a legal tow weight for a C10. There are several factors you need to consider or can use to determine the safe tow weight for your truck::
• Gross Vehicle Weight Rating (truck weight + accessories + cargo + tongue weight cannot exceed this number)
• Gross Combined Weight Rating (truck weight + accessories + cargo + trailer/load weight cannot exceed this number)
• Maximum axle weight rating - The maximum allowed weight each axle can safely carry. These numbers combined should equal your GVWR, but limits how that weight can be distributed.
• Tire weight ratings - The maximum weight each tire can safety carry. These ratings should exceed GVWR when combined and each pair of tires on an axle should exceed the maximum axle rating.
• Maximum hitch towing capacity - The maximum amount of towed weight that can be safety attached to the hitch (or bumper). This number should be stamped on the hitch, and is usually the limiting factor on lighter duty towing systems.
If your load exceeds ANY of these stated limits, you are unsafe to tow.