I was actually in a similar situation except... from your sister's perspective. My brother is about a decade older than me and has treated me horribly all my life. Yet, for whatever reason, all I've ever wanted was him to maybe sit down and watch a series with me. In fact, when I was considerably younger, I learned from one of his friends that he liked Fist of the North Star -- so I purposely found someone I could borrow fansubs from and started to watch them whenever he was around.

...Even now, about 6 years after I attempted that, I still wish he would've just sat down and watched even a couple minutes with me so I could at least remember something we did together (something that didn't involve him being an asshole to me, at least.)

/sob story