You are assuming it is overweight due to the materials used in the build, I guess?
I didn't use any lightweight wood in my last conversion - combination of pine wood, solid standard plywood and IKEA cabinets plus a solid wood kitchen worktop.
Came in at 2,800Kg on a 4600Kg chassis.
Not sure what the " Weighbridge CertViewings by appointment only" comment is meant to mean? Maybe it was weighed and is close to a limit? I doubt Motorhome Depot would list an overweight van if they actually knew it was overweight?