"Supra" means "Above". So, why use "Supra"?
Reason #1: "Supra" has a specific legal meaning, while "Above" can be ambiguous;
Supra always means a prior part of a written text (ie, "above this paragraph").
Above usually means a prior part of a written text (ie, "above this paragraph").
However, sometimes, Above means a higher court (ie, "the appellate court").
Reason #2: "Supra" is a short/simple word (compared to other latin terms);
Reason #3: Using "Supra" will indicate that you are willing to fight to the end.
Fighting to the end ≈ going through the appellate process.
Example A (An Ambiguous use of "Above"):
"Fact 555: Plaintiff had blah blah blah..."
"Law: The court above says that Plaintiff deserves X-Y-Z (see Fact 555, above)."
Analysis:
This passage used the word "above" twice in one sentence. The first time it meant an appellate court; and the second time it meant a previous portion of the same document.
Problem:
Ambiguity.
Moreover, every subsequent citation of that passage will increase confusion.
Solution:
Use "supra" instead (see Example B, infra)
Example B (Clear use of "Above" and "Supra"):
"Fact 555: Plaintiff had blah blah blah..."
"Law: The court above says that Plaintiff deserves X-Y-Z (see Fact 555, supra)."
Analysis:
This passage cites itself; while making clear that its legal application comes from a higher court.
Benefit:
Clear. Simple.
Both the appellate court and the trial court will understand what you're saying.