The metric unit that is used to describe weight as a measure of the force of gravity is called a Newton.

That is true. Force is mass*acceleration, and the units for any type of force is the Newton, (N) which is named after Isaac Newton).

The Newton is actually the simplified version of kg*m/s^2. So instead of writing kg*m/s^2, in which kg (kilgrams) is mass and m/s^2 is the unit for acceleration, we can write Newtons (N).