I think Ron is correct, you need to find out exactly the what & why of the restrictions for the form you signed.
While I do not live in California, and therefore am not familiar with all of their requirements, my thoughts is that the 10,000 lb limits may be in regard to the Gross Vehicle Weight (GVWR) rating and may be the maximum loaded weight of your truck it's self generally based on axle weight ratings (or it may just be one of those Gov Reg's to get additional fees).
There is also a Gross Combined Vehicle Weight Rating (GCVWR) which refers to the combined truck and trailer weight. In your case you may find that IF your vehicle in fact has a GVWR of 7100 lbs, it also has a tow rating as well (not to be confused with hitch rating).
If you were to find your truck was rated to tow a 10,000 lb trailer, then your gross combined rating could be 17,100 lbs.
Generally, in most states a gross vehicle weight or gross combined vehicle weight over 26,000 lbs, requires a commercial drivers lic (CDL). There are exceptions for non commercial (as in RV use) where you can exceed that 26,000 lb. limit and not require the operator to have a CDL (as long the vehicle's official weight ratings, located on the vehicle, are greater that what you are operating the vehicle/trailer at. However, even if you are operating as a non-commercial class (ever notice the "Not for Hire" markings on rigs), you could, if stopped for some reason get a ticket if found to exceed the rigs "rated" weight limit.
There should be a sticker on your truck door jam with both tire pressure recommendations and axle load limits along with the gross vehicle weight limit. Usually the gross combined info is found in the owners manual.
Another area of concern for larger rig's is the overall length limit which is typically 65 feet. There are exceptions to this but this area has created problems as well as being easy to spot.
Rich Powers