The term "pounder" in reference to bore size is actually a lot like the term "gauge" in reference to shotguns. A 12-gauge shotgun, for example, has a bore of such diameter that a lead sphere of the same diameter would be 1/12 of a pound, or it would require 12 of them to equal one pound of lead.
Likewise, a "16-pounder" artillery piece has a bore diameter such that an iron ball of the same diameter would weigh 16 pounds. (I think it's iron, anyway. Maybe someone else knows different.)