Usage of the phrase " just because" at the end of sentences
Solution 1:
How? Just because...
Sorry, I couldn't resist. I don't have an ANSWER, but I have a theory. I think the phrase is verbal shorthand, that has no proper literary form. What I mean: I believe the phrase may have come from people saying "because... because..." not having a reason, then "just because!"
Solution 2:
The Urban Dictionary defines "just because" as meaning "because you could".
It's really just a 'circular' response:
I did it because I could do it (no other reason)
He did it because he could do it (no other reason)