It's kind of an unofficial family tradition I guess, and it probably has a lot to do with holding onto collegiate days. I'm not sure if any other families in my chapter did this, but some of the girls in my family started wearing something besides their lavalier when they began their senior year, as did some other girls in other families. I gave mine to my second little at our senior ceremony when I graduated since she still had two years to go. Normally in my chapter though, your Berry Buddy is supposed to buy it for you when you get initiated, but I knew I would be graduating the semester I took my second little so I never got her a Berry Buddy (lazy senioritis perhaps). Your Berry Buddy is selected by your big and does a little clue thing during Link Week (week prior to initiation) and right after you're initiated and get your gifts from your big, your Berry Buddy reveals herself by giving you your lavalier. Your Berry Buddy is someone that is close to your Big and is supposed to serve as a sort of surrogate Big if you're ever not available for her. It's usually someone not in your family (though I suppose it could be, especially in my case since my two littles got so close they won Frick and Frack after I left).
Whew, sorry that was kind of a long explanation!