Why does Chabad and some Chassidim wear bigger / larger Tefillin batim / boxes? 

Generally speaking yes, but not necessarily. I discuss the reason in the video.

@@TheSoferCenter I didn't see anything about the size of parshyot. I would think putting small parshyot it big batim would be yuhara.

The point is the bigger Batim. I'm not aware of any issues of putting smaller Parshios in larger batim The only thing you have to be careful about is because they're smaller Parshios extra effort has to be made to make sure that they're packed properly so that they don't flip over.

😅😅 Fake news