In America, we say your argument doesn't carry (not hold) much weight. However, we also say, your argument doesn't hold water (meaning that it has holes in it.)

If I tell you that "your argument doesn't hold (or carry) much weight", it means that I (or other people, depending on context) do not assign much importance to what you are saying. It does not mean that I think your argument is wrong. I could even agree with you completely. It just means I am not (or other people are not) listening to what you say. Here's an example. An old fool knows that there is a hole in a dam and the town is going to be flooded. He is right. Everyone is going to die. But nobody listens to him because he is an old fool and so his arguments don't carry any weight.

not valid

It doesn’t make sense. It can’t be justified.