As for equal protection, this applies in this case also because the law didn't apply to all sugary(I hate that expression, actually)drinks equally, therefore the manufacturers of certain drinks were not afforded equal protection, or should I say some manufacturers were held above the law, which amounts to the same thing.
As to the first section of the Fourteenth Amendment applying, I don't think it does. Here is the text:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
The context was in regard to protect the rights of former slaves from the states that had slavery. The "equal protection" part I think obviously means that people are protected equally, as oppose to beverages being protected equally. However the part that could be used by the judge in this case (and might have as far as I know) is:
No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States;
I am not convinced this could extend to soft drink sizes being limited by a state as being one of the "privileges or immunities of the citizens of the United States", but I am not exactly prepared to argue that it is definitively not...just that it seems a bit of a stretch.