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sum

In England, 15ᵗʰ – 17ᵗʰ centuries, a unit of count for nails, = 10,000 nails. Also spelled somme and summe.

T. S. Willan, editor.
A Tudor Book of Rates.
Manchester (UK) University Press, 1962.

Page 41.

sources

Copper nailes Rose nailes & Sadlers nailes the sum cont. ten thousand…
Harness nailes the sum cont. ten thousand…
Spring nailes the sum cont. ten thousand

“A Subsidy granted to the King of Tonnage and Poundage and other summes of Money payable upon Merchandize Exported and Imported.”
A statute from the 12th year of Charles II, 1660. The selection is from the Booke of Rates, which is not part of the statute proper but developed from it. Both are printed in:
Statutes of the Realm, Volume 5: 1628-80, John Raithby, editor.
London: 1819.

Nalys by the Summe. Also there ys a numbyr whiche ys called a summe; and hytt conteynythe x^M lbs.: and therby be sold paten nayle, sadelers' naylys, cardemakers' nalys, and dyuers odyr.

Nails by the sum. Also there is a number which is called a sum, and it contains ten thousand pounds, and thereby are sold paten nails, saddlers' nails, cardmakers' nails, and divers others.

MS. Cotton, Vesp. E. IX (15ᵗʰ century). See Hall and Nicholas, page 17.

Despite the “lbs.”, other sources (and even this one, implicitly) suggest the sum was a unit of count, not mass. Ten thousand pounds of nails would be a very unwieldy quantity. The “lbs.” is probably a copyist error.

The paten is the dish upon which the bread is laid during Mass. Usually they are made of metal; we don't know what a “paten nayle” is.