Advice on giving Ribbons unique benefits from Gym Badges?

I'm writing a story where a girl who recently moved from the Kalos Region to Sinnoh decides to become a Coordinator. She accidentally finds her first Pokemon in Riolu after discovering it injured in a field when she's attempting to help her dad with some catering deliveries. She catches an Eevee before deciding to participate in her first Contest.

Her twin brother who pursues Gym Battles joins her on her journey. He does them because he enjoys getting stronger and becoming the Champion is the ultimate symbol of strength in his mind. I decided that I would take a plot point from the manga where earning Badges makes Pokemon slightly stronger on top of making them more obedient. However, Contests, at least in the games, only increase friendship, and also affection in Gen 6.

I just need some tips for making Ribbons more beneficial.