kg is indeed mass and mass is a measurement for the matter an object contains. It's a definite amount for any given object. SI unit is kilogram or kg

Weight is a measurement of gravitational forces on mass. Weight is relative to location due to changing gravitational forces (expressed as acceleration or distance (m) divided by time (s) squared). SI unit is kg•m/s^2 or mass times acceleration (which is the units used to express gravity or g).

So every time we waddle our large bodies onto a scale it's figuring out a number which (should be anyway) your body's mass times Earth's gravitational force 9.81m/s^2 and expressing it in kg because we are silly creatures.

Silly but also practical and/or self-absorbed. So much so that we made 1g = 9.81m/s^2 conveniently our home world's gravitational force! So since weight is relative, and depends on a definite value of mass (m) times the variable value of gravity (g) you can kinda sorta just eliminate g when considering weights compared on earth taken at the same location. Since g = 1 you get weight= mass • g or weight = mass • 1g or weight=mass(times Earth's g...but no one says that part. It's assumed). So on earth, at the same location, two objects with the same mass also weigh the same absolute number of units, but the units are technically different, just never or rarely expressed differently. We just assume for the sake of simplicity (but also confusion!) being on earth that mass=weight.

Why did I type this? I don't know! I hate myself probably. And if anyone comes in quoting equations and saying mass varies depending on certain conditions, I promise I'll start crying.