I think the solution might be
I killed my brother a long time ago:
The brother that was killed would be believe, as facts kill believes, either by turning them into knowledge, or by disproving them. Starting to disprove believes by facts indeed started a long time ago, in Greek philosophy.
And if I'm right, running fast won't help you:
You cannot escape the hard facts (I take "running fast" as metaphorical here, like running from the truth).
My relatives are weaker, shorter:
Relatives might be believe, hypothesis, assumption, possibility — all are weaker than a fact, as they are less certain. I have no idea how "shorter" fits in, though.
But I may be wrong alone:
A fact can in general only be decided in a context. For example "it is raining" may be true or false, depending on whether you are saying it on a rainy day or on a sunny day.
Many facts are hard to decide.
The riddle has the science tag. Science is all about facts.