Which regulations require the ARROW documents?
It is in several places:


Airworthiness Certificate  FAR 91.203
Registration Certificate FAR 91.203
Radio Station License (international flights only)
Operating Handbook FAR 91.9
Weight and Balance FAR 23.1589


CFR 91.9:


  (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.
  
  (b) No person may operate a U.S.-registered civil aircraft -
  
  &nbsp;&nbsp;(1) For which an Airplane or Rotorcraft Flight Manual is required by § 21.5 of this chapter unless there is available in the aircraft a current, approved Airplane or Rotorcraft Flight Manual or the manual provided for in § 121.141(b); and
  
  &nbsp;&nbsp;(2) For which an Airplane or Rotorcraft Flight Manual is not required by § 21.5 of this chapter, unless there is available in the aircraft a current approved Airplane or Rotorcraft Flight Manual, approved manual material, markings, and placards, or any combination thereof.


CFR 23.1589:


  The following loading information must be furnished:
  
  (a) The weight and location of each item of equipment that can be easily removed, relocated, or replaced and that is installed when the airplane was weighed under the requirement of § 23.25.
  
  (b) Appropriate loading instructions for each possible loading condition between the maximum and minimum weights established under § 23.25, to facilitate the center of gravity remaining within the limits established under § 23.23.


FAR 91.203


  (a) Except as provided in § 91.715, no person may operate a civil aircraft unless it has within it the following:
  
  (1) An appropriate and current airworthiness certificate. Each U.S. airworthiness certificate used to comply with this subparagraph (except a special flight permit, a copy of the applicable operations specifications issued under § 21.197(c) of this chapter, appropriate sections of the air carrier manual required by parts 121 and 135 of this chapter containing that portion of the operations specifications issued under § 21.197(c), or an authorization under § 91.611) must have on it the registration number assigned to the aircraft under part 47 of this chapter. However, the airworthiness certificate need not have on it an assigned special identification number before 10 days after that number is first affixed to the aircraft. A revised airworthiness certificate having on it an assigned special identification number, that has been affixed to an aircraft, may only be obtained upon application to an FAA Flight Standards district office.
  
  (2) An effective U.S. registration certificate issued to its owner or, for operation within the United States, the second copy of the Aircraft registration Application as provided for in § 47.31(c), a Certificate of Aircraft registration as provided in part 48, or a registration certification issued under the laws of a foreign country.


The other "R" for the radio station license was in the FCC documents, but since it is no longer required, it does not appear. If you are operating within the United States, the acronym is AROW. Outside of the United States you would have to see the Canadian, Mexican, or other countries requirements. Here is the Canadian information as an example.