With the old company logo on the side of the trailer I'm guessing that if you look like your over the min required weight based on the state your in..... you'll draw the attention of the commercial driver enforcement officers that will see you from state to state..... You need to be able to prove that your "not for profit", "commercial" to them..... any load that is for profit..... requires correct license, permits, etc..... including the licensing of the truck, trailer and your drivers license.....
This commercial drivers information is stored in a national data base and is available to enforcement officers in any state based on your drivers license, or plate number... .
I would suggest that you remove the logo from the company that owned the trailer before you... . If you contact your local state police, commercial vehicle enforcement division, they will answer your questions... .
Hope this helps.....