There is nothing specific saying you have to do a weight and balance but you have to " determine " that you will be within all limitations. So, if an inspector were to ramp check you and he asks how do you know you comply with all the limitations (Max takeoff weight, max ramp weight, C.G. within operating envelope, ect...) in your aircraft flight manual you better be able to show something. If not and you are exceeding any limitation they can nail you with violating 91.9 (see Below) and our favorite 91.13 careless and reckless operation.
91.9 Civil aircraft flight manual, marking, and placard requirements.
(a) Except as provided in paragraph (d) of this section, no person may operate a civil aircraft without complying with the operating limitations specified in the approved Airplane or Rotorcraft Flight Manual , markings, and placards, or as otherwise prescribed by the certificating authority of the country of registry.
I hope this answers your question.
Deltoid