The longest time a football game can be delayed for weather depends on the gravity of the situation. It can last for approximately a couple of hours.
The major scenario taken into account while calling for a delay in the kickoff time is the safety of players and others involved. The extreme weather situation falls under Article 4 of the NFL rule book.
As per the 2022 NFL Rulebook, emergency situations, namely lightning, flooding, extreme atmospheric conditions, and power failure, can cause delays in the commencement of the fixture. It mentions that all fixtures must reach a conclusion, except in emergency situations.
The Commissioner and other appointed representatives are the governing bodies who inspect the situation and take necessary actions. They are also given the power to call off the match.
The Referee gets the duty to authorize delays in the match if the Commissioner or the representatives are not in attendance. For that, he needs to consult with the primary authorized personnel through any means and come to a conclusion.