Great question. Maybe a reflection of where a person is in the lineage of Griz basketball. If you come to the program recently, I am not sure how it ranks.
Weber State is the flagship basketball program in the Big Sky. They have been the most consistent over teh years, and because Montana rarely has been horrid in basketball those games have mattered a bit more. The rivalry aspect has picked up recently because of how good both programs have been over the past four or five years.
That hasn't always been the case for MSU and UofM. Those games always have an instate rivalry feel, but even much of that has dissapated in the last decade or so. Went to a MSU game before I left Montana and there were 4,000 people at the game. I know that has changed in recent years, but the punch of the game is gone. Definately not 80's with LK, Ferch Brothers, Damako, McGowan and so forth. That Montana flavor of the game is a gonner.
I think my understanding of the rivalry is as much as a reflection of where UofM basketball is now. Nostaligcally, I think MSU is probably 1 and Weber State is 1A. Yet, in terms of current relevance Weber State over the past four or five years has held more value as a basketball game.