In physics, how are two quantities found to be proportional to each other? [closed]

For instance, force was discovered to be proportional to mass and acceleration.

How are these proportional relationships discovered and proven to be true?

I think that the problem is that people think that $$F=ma$$ is a law (and needs a proof) while it is a definition of $$F$$ and $$m$$, so does not require a proof.