1) General references
a) Don't use the term "weight stations" - they were defined as weigh stations, but now are officially titled as Motor Carrier Service Centers.
b) Regarding your truck: you may privately own it, but so do commercial trucking businesses privately own their company trucks. What determines a "commercial vehicle" is the VDOT definition seen in the following link - your vehicle is a commercial vehicle.
2) Virginia Law
Don't ask a LEO or accept a LEO's word on what the law is. In this case (firearm in your truck/commercial vehicle), there is no statute in the Code of Virginia that says you cannot. The absence of a law saying that it is illegal leaves such by default to be legal.
Use Code of Virginia search box, top right of page
3) In support of Virginia state law
a) DMV is responsible for administering Virginia's weigh stations. For more information, contact DMV's Motor Carrier Services Division at 804-249-5130. (DMV in this case refers to the Virginia Dept. of Motor Vehicles)
b) Inspectors from the Department of Motor Vehicles were transferred to the Department of State Police and received training at the State Police Academy. After 12 weeks of instruction and graduation, Weight Enforcement Officers were assigned to the 11 weigh stations across the state for the purpose of enforcing commercial vehicle laws - 1982
c) The title of Weight Enforcement Officer was changed to Commercial Vehicle Enforcement Officer - 1993
d) Commercial Vehicle Enforcement Officers (Va State Police) working at weigh stations, also called Motor Carrier Service Centers, make sure that trucks comply with state and federal rules.
4) Federal Law
There is no federal law restricting guns in commercial vehicles. Again, the absence of a law leaves the de facto result of not being illegal. Motor Carrier Safety Improvement Act of 1999 - Public Law 106-159 (113 Stat. 1748) creating the new Federal Motor Carrier Safety Administration who is responsible for overseeing motor carrier and driving laws.
Repeat - there is no rule from FMCSA (Federal Motor Carrier Safety Administration) making carry of a gun in a commercial vehicle illegal.
5) Carry permits
a) If the state that issued your CCL is covered under reciprocity with or by recognition in Virginia your permit is legal in Virginia.http://www.vsp.state.va.us/Firearms_Reciprocity.shtm
b) Note that you do not need a permit to OC (open carry) in Virginia, including in your truck.Refer to §§ 18.2-279 to 18.2-311.2. The Code of Virginia may be searched at http://leg1.state.va.us/000/src.htm.
6) Sample Experience
You should reread post #10 in the following link - you posted to that thread so should have read his reply.
It is not illegal to carry in a commercial vehicle in Virginia; however, an employer may have rules against the practice for company drivers and contractors + there will still be places that guns are not permitted i.e military installations.
More than you wanted? Surely not more than you need.