I was wondering if there is a disposition for small claims court that
was settled via arbitration (no appeal is allowed and the decision is
final) - then would it be unlawful to pay more than the extra amount?
Normally, when a case is resolved via arbitration, the arbitration award is filed with a court together with a motion to "confirm" that arbitration award. This is what makes an arbitration award enforceable by means of legal process such as garnishment and levying on assets. An arbitration award determines the rights of the parties, but usually provides not means by which the award can be collected independent of an ordinary court.
When the full amount owed under a money judgment, whatever its source, is paid, the person to whom the judgment debt is owed has a legal obligation to file with the court a document called a "satisfaction of judgment" (that also releases any liens arising from the judgment) indicating that the judgment has been paid in full. The person to whom the judgment debt is owed can be compelled to execute a satisfaction of judgment in court, with proof of payment, if the person to whom the judgment debt is owed fails to do so, in post-judgment motion practice in the court in which the judgment is entered.
It is not "illegal" to intentionally or unintentionally pay someone to whom you owe money more than you actually owe to them. Indeed, it isn't uncommon to do so, to eliminate all doubt that the judgment has been satisfied in the face of, for example, potential discrepancies in post-judgment interest calculations due to rounding errors or the application of the wrong compounding of interest rules.
An overpayment margin of error is desirable because, if a judgment has not been fully satisfied, even by 5 cents, for example, that could cloud the title of property of someone who purchased property that was subject to a judgment lien arising from that money judgment, which would have many important procedural implications in a subsequent foreclosure by a new lender against the property who would be subject to second mortgage foreclosure rules rather than first mortgage foreclosure rules.
The only legal question presented by an overpayment of a judgment debt (again, the source of the debt doesn't matter), is whether, under the particular circumstances under which a judgment debt is overpaid, the person making the overpayment has a legal right to a refund of the overpayment, possibly through post-judgment motion practice before a court, through arbitration, or through a separate lawsuit.
If the amount of the overpayment is "slight", ordinarily it would not be cost effective to bother, since it would require expensive and rather complicated and lawyer intensive resolutions question of obscure civil procedure rules. Instead, the person who was overpaid would get to keep the slight amount of money that was overpaid.
This may come into play during legal tender issues and denomination of
the currency and when relating to the Coinage Act of 1965 in the U.S.
I would like to know how this would affect repayment for the defendant
if the said defendant needs to pay out the arbitration ruling.
I can't imagine any circumstances in which the Coinage Act of 1965 would be relevant to this question. Maybe there is one, but I can't think of one, and I can't follow your reasoning regarding why anyone would think that this is relevant. Perhaps a hypothetical example would clear up why anyone could think that this might be relevant.