Heres a picture from the bottom

Pairpoint was founded in 1880, so the 1816 is definitely not the date of manufacture. Your pot has elements of the aesthetic style, so it was probably made early in the company's history.

It's their model number, probably.

Its the pattern, or style number and is silver plate (quadruple plate). This style was popular from the late 1800's thru the early 1900's. It would have been used on a regular basis as a daily coffee pot.