In Japanese competition there are two types of matches; one where both fighters take offensive roles, and the other where one aggressive, offensive fighter competes against a defensive type of opponent.  In both types of competitions the owner and spectators decide the length of the match based on their level of satisfaction, and most matches may last anywhere between 60 and 90 minutes. 
In the first type of competition where both fighters take offensive roles, the heavier cock wins if it is able to knock out the lighter bird within a predetermined time frame.  If the lighter weight competitor is able to stay standing throughout the length of the match without escaping, it is then declared the champion.
In the second type of match, the owner pronounces their fighter as either offensive or defensive.  In such a case the weight of the fighter is deemed irrelevant, but the offensive competitor must knock out the defensive opponent within a set time frame to win the match.  The heavier the competitors, the longer the match, and the lighter the competitors, a lesser amount of time is determined for the necessary knock out.  The match may also be cut short or lengthened depending on the true weight of the bird.  In some cases, owners may not allow their fighters to compete if they are dissatisfied with the proposed opponent or length of match time.  This is all merely down to the respective strategy and tactics of each owner.