Jason is, in a sense, an exaggerated male version of Lorelai. They both share a similar sense of humor, and he is very "off center", as Lorelai at one point describes it to Rory. Jason has worked at his father, Floyd Stiles's, company since he was very young and is a Harvard graduate.
Jason reveals to Lorelai in an episode that he is an extremely light sleeper and cannot sleep with anyone else, and Lorelai has to sleep in a guest room, which houses his "distractions" like films and books. He has a very strange dog named Cyrus, which has the ability to stay remarkably still without moving and making any noises, which is what Jason loves about him.
Jason is Richard's business partner through Season 4. He also dates Lorelai, making him her last boyfriend before she begins dating Luke. Jason initially teams up with Richard in the hopes of trying to defeat his father's company. However, Jason has a huge falling out with Richard after Jason's father, Floyd Stiles, threatens to destroy Richard's business. Richard, in turn, makes a deal with Floyd that leaves Jason out in the cold. Jason sues Richard, which prompts Lorelai to break up with him. Jason is seen one last time at the Dragonfly Inn, trying to reconcile with Lorelai, which fails.
Jason has a passive-aggressive antagonistic relationship with his father, whom he usually refers to as Floyd. Although he does call him Dad when he furiously races after Floyd following the latter's proclamation that he is suing Jason and Richard's company. Jason's mother appears somewhat passive in her one appearance, although Jason mentions several times to Lorelai that he speaks to his mother. Jason never refers to her by her first name, although he does not speak of her with respect either, mentioning to Lorelai that she takes 'happy pills' and insinuating the pills make her unable to converse at her normal standard.
Jason seems to respect Richard's business fervor and shows loyalty to Richard over his own father. Richard entertains the idea of Jason's business while Emily is indignant at Jason's relationship with his family, and Richard seems to like Jason, yet is not hesitant to sell Jason out once his and Emily's livelihood is endangered, effectively ending their business and social relationship.
They meet as kids at summer camp and while canoing, Jason apparently stands up to tip Lorelai into the water to make her shirt see-through. Such a gentleman. While it's not certain if Digger is a name Jason sustained at camp, he does call Lorelai by her camp name (assumably) when they meet in 2003 as adults. Jason is immediately crass about Lorelai's looks, and obviously infatuated and pursues her for a date.
Lorelai is hesitant because Jason belongs to the world of riches she wants to leave behind, but agrees after a nasty confrontation with her mother, to go on their first date. As they continue to date, Jason wants to announce it to Emily and Richard, but Lorelai is afraid of letting her parents into her personal life. Jason has trouble with this, but agrees to appease her. While Lorelai states on many occasions she finds Jason weird, they have a rhythm that both enjoy and perhaps Jason is a bit more committed to their relationship than Lorelai is.
- Richard – You hate your father that much?
- Jason – I don't hate him. I just don't wanna be him.
- Jason went to Harvard, although his father, like Richard Gilmore, is a Yale alumnus. This is similar to Lorelai's approach to discern her life from that of her parents.