Generally speaking, you are not commercial. However, you need to pay attention to the location of the sign(s).
For example: Many residential areas will have signs like that to keep large trucks from driving through.
Sometimes business areas restrict commercial vehicles to specific streets.
As previously noted, if you see a sign restricting a bridge to 10,000 lbs., you don't want to try it with a 20,000 rig, commercial or not. The consequences could be like the one in Mt. Vernon WA.
Some roadways are not designed/built for vehicles weighing over 10,000 lbs. and are signed appropriately. Believe them.
Kinda like the height restrictions "Large,Tall Trucks restricted" Well, I'm not a truck, but I am 12'3" high and a 12' underpass would take my roof off as easily as a trucks.
In California, before RVing was so popular, the speed limit for vehicles towing or 3 or more axles was 55 mph. The signs said Trucks, Autos Towing 55. (Speed limit is still 55)
So,guess what? Boat trailers, RV trailers said "I'm not a car or truck so it doesn't apply to me.
CalTrans finally got the message and changed the signs to read:
ALL VEHICLES TOWING 55. Boat trailers and RVers still ignore it, thinking it doesn't apply.
In the case of a weight restriction, I would be very careful about driving a highway with a 10,000 lb. limit. I wouldn't want to take the chance. Just because my 26,000 lb. MH is not commercial doesn't mean it doesn't weigh 26,000 lb.s