Truth is, nobody is going to forego a higher iLvl slot piece for a lower one with "better stat weight" (if they even knew what it was), especially not when the game itself distills your role potential into a numeric stat (i.e. iLvl) and locks you out of content based on this number. Using a bit of an extreme scenario here, but if you were on the border ilvl for a particular content, that is the only thing which determines whether I'm "good" enough to qualify for certain content or not regardless of stats and their weights.. which suggests that as long as the iLvl is higher, I'm safe.
Now, if we had multiple items at the same iLvl (which rarely ever happens), maybe i'd make a case for the importance of stat weight.. but its otherwise not something i've ever paid attention to, other than that 1 time I was figuring out what to meld into my new weapon. I can't be the only one.