This must be the CapnR Legal Dictionary. I note the glaring lack of a citation to any real legal dictionary.
Viz. Videlicet, that is to say.
SOURCE: Bouvier's Law Dictionary, 1856 edition.
Videlicit. Lat. The words "to-wit," or "that is to say," so frequently used in pleading, are technically called the "videlicit" or "scilicet;" and when any fact alleged in pleading is preceded by, or accompanied with these words, such fact is, in the language of the law, said to be "laid under a videlicit." the use of the videlicit is to point out, particularize, or render more specific that which has been previously stated in general lauguage only; also to explain that which is doubtful or obscure. Its common office is to state time, place, or manner which are of the essence of the matter in issue.
SOURCE: Black's Law Dictionary, Sixth Edition
Webster's New World College Dictionary, 4th Edition:
viz. abbrev videlicet; that is; namely
You don't need a legal dictionary. It is clear from the text exactly what is being said. The listing of the state names after "viz" was to clarify the mean of the term "the said United States."