Your photos showing the ball's "approximate" weight and diameter measurements are helpful, and I thank you for already providing that info.

As NOLA_Ken said, those preliminary measurements are in the ballpark for a 1-Pounder caliber cannonball. That caliber was used from the Colonial era to the end of the 1830s, when it fell out of favor due to the advent of more-powerful cannons in the run-up to the civil war.
www.civilwarartillery.com/shottables.htm
Because most 20th-Century "iron" balls are actually made of steel, and no cannonballs made of steel ever got used in America, we need super-precise measurements so we can know with certainty whether your ball is an iron one or a steel one. Unfortunately, spring-type analog scales like the one in your photo are not precisely accurate enough to be trustworthy for authenticating a cannonball. You'll need to use a digital Postal Shipping scale.
The dial-face analog caliper you used is accurate enough for relic authenticating... but we need you to measure two spots on exactly-opposite sides of the ball which have no rust/dirt encrustation on them.
Also, it is helpful to measure the diameter of a "maybe-cannonball" on several directions, to make sure it is a True Sphere... not significantly out-of-round. Being out-of-round could cause a cannonball to jam in the cannon's bore upon loading or firing, so all actual cannonballs were very carefully manufactured and inspected to be perfectly round.
Please do the super-precise measuring with a digital Postal Shipping scale, and re-measure the ball's diameter on some spots that are free of rust/dirt encrustation, and let us know those new measurement numbers.
Meanwhile... here's some reading which you may find to be educational. I co-wrote an instructional article with David Poche on how to correctly distinguish ("authenticate") actual cannonballs from the many imposters... such as mining-&-stonemilling industry rock-crusher balls, gatepost tops, sports shot-put balls, counterweight balls, etc. Go here:
SolidShotEssentialsMod