Don’t distress yourself too much, on approx 50.000 Km allover Africa (2003 -2006) in a 12ton truck we have never been weighted! Slow down, pass the queue, get eye contact to the “officer” (if there) and after they had noticed (sooner or later) your vehicle as a tourist one they typically wave you through. Finally you don’t have a commercial car, so even if they pull you over (never done with us) this should have no consequences.
Keep in Mind: none of the “road officials” in Africa is used to a camper truck, so sometimes you have to bring some kind of evidence…e.g. a typical conversation on nearly every Sudanese toll booth:
Officer: “Good morning, sir! How many peoples?”
Tourist: “Good morning, officer, just we two.”
Officer: “How many in the back?”
Officer: “None?! How many cows?”
Officer: “None?! How many goods?”
Tourist: “No goods.”
Officer: “What’s in there?”
Tourist: “Just a kitchen, it’s our house, we live in this car!”
Later, after opening the rear door and when the excitement about the “car with a sink” had calmed down, they let you go, usually paying just the car fee (if you are lucky).
Enjoy your time in Africa
Ps: take it slow, there are lots of speed traps in TZ! ;-)