Haven't you heard the phrase "weightless in space"? Things have mass with out gravity, but with out gravity they have no weight.
If I am ever in doubt about what I am dealing with, be it statics and dynamics or heating and AC, I always look at the dimensions of what I am dealing with. It's called dimensional analysis.
With this weight-force scenario it does take some discussion in the classroom for everyone to get on board. I still don't remember what a pound is compared to a pound force. I do remember the differnece between a Kg and a newton though. And that is the difference between mass and weight(force).
When someone says "it weighs 5 Kgs". We know what they mean but they are technically wrong. They mean it weighs 5kg. at the surface of the earth. Whcih is really measured in newtons. Kgs have no force component in the dimensions.