Scales are for commercial trucks. That means, for hire. There is also a minimum weight. I don't suspect you are hiring out so you wouldn't have to stop. Call your state's commercial vehicle enforcement division to find out for sure.
If everybody towing a trailer had to stop at a scale, it would be crazy. Could you imagine all the RVs etc. piled up waiting to be weighed?
If your new to towing, a few suggestions
1. Slow Down
2. Does the trailer have brakes? If so, make
sure sure you have a controller to use them.
Its bad when your trailer gets ahead of you.
3. Be carefull of where you go. A long curvy
DEAD END road can cause many headaches
when you have to back out.
4. Check tires and wheel heat when you stop.
There can be problems with underinflated
tires, bad bearings and sticking brakes.
5. Its going to take longer to stop and a greater
distance to turn.
6. Use your mirrors.
I am sure others will have recomendations also.
Enjoy the trip. What year Camaro. To this day I kick myself for selling a 69 RS I had.