Honestly, at least in most of my friend's fraternities (not mine of course
), the "Big Bro/Little Bro" thing is primarily intended as a support channel to get you through Hell Week, get you a sweatshirt, he gets a paddle out of it he can hang on his wall, and then from there it is moot. I got along with my big and my little, but neither was THE friendship in my fraternity and eventually I got much closer to other guys in the house, and so did they.
Having a certain big or little is not an automatic ticket to a deeper friendship with him over everyone else in your house, and is not an automatic ticket to him having a deeper bond with you over everyone else.
Tons of guys have multiple little bros. Tons of guys never even get one. By trying to force it to be this mystical bond type of relationship, you're probably pushing him away more than anything.
It's not that serious.