Does Koyomi ever get more powerful in the Anime or Light Novels?
You are wondering how can he can


   tell his sisters that you have to be strong to be a hero despite being rather weak himself.


But does he ever


   claim to be a hero?


I can't recall that he did. Thus, there is no discrepancy in his words and the story he sees in himself is not invalid.

His sisters, however


   did, quite proudly, claim to be heroes. He only (rightfully in his opinion) pointed out that they can't live up to that standard.


On a meta level: Not every story needs a strong hero - many great pieces (commonly for adults) rather tell about the weaknesses of a person rather than their strengths. I would consider Monogatari well fitting in this light.