You're "over-simplifying" it. I didn't read these rules you speak of, but they probably don't address, explicitly, a minimum weight, because the weight is defined by the division. You can't be under the weight division's stated weight parameters, or you will not be fighting. You show up to a welterweight title fight weigh-in and tip the scale at 154 pounds, I don't think the commission is clearing you to fight.
You see, "you think" or "don't believe" are the phrases that completely nullify the argument. The reason you see the minimum and maximum is because some really "slow" people don't understand that one pound, over the limit, pushes you to the next weight class. I will "cut and paste" for you so that you may take a look at a PECULIAR detail that is left out.... A MINIMUM FOR THE STRAWEIGHT DIVISION. Curious, no? Why do you think they left that out?
2. Weight Divisions
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Except with the approval of the Commission, or its executive director, the classes for mixed martial arts contests or exhibitions and the weights for each class shall be:
Strawweight up to 115 pounds
Flyweight over 115 pounds to 125
Bantamweight over 125 to 135 pounds
Women's Bantamweight over 125 to 135 pounds
Featherweight over 135 to 145 pounds
Lightweight over 145 to 155 pounds
Welterweight over 155 to 170 pounds
Middleweight over 170 to 185 pounds
Light Heavyweight over 185 to 205 pounds
Heavyweight over 205 to 265 pounds
Super Heavyweight over 265 pounds