relationshippy
adj. Relating to something that is associated with or strongly reminiscent of a romantic relationship.
Also Seen As
Examples
2008
To refresh your memories, the "Grey's Anatomy" co-star was widely viewed as dissing her fellow cast members and in general the hand that feeds her when she opined that the show's scripts last season didn't merit her getting an Emmy nomination. Blogs cited "Grey's' insiders" who reportedly were ticked off, and betrayed fans of the relationshippy doctor show are treating Heigl (who plays Izzie Stevens) like she was the second coming of Dixie Chick Natalie Maines.
—David L. Coddon, “Hard to knock Heigl for just speaking candidly,” The San Diego Union-Tribune, August 15, 2008
2008
Q: I've been friends with this girl for years and we have a good time together. We started sleeping together. Then she abruptly wanted to stop the physical activity, which is fine, but:

She wants to break it off because she thinks I'm being too "relationshippy" too quickly because I invited her on a trip, but really, as a friend, I would have invited her anyway and it wouldn't have been weird, but now it is because we slept together.
—Shawn, “Definitely maybe,” Star Tribune, March 13, 2008
1991 (earliest)
George: I got it. You wanna get her something nice? How about a music box?

Jerry: No, too relationshippy. She opens it up, she hears that Laura's theme, I'm dead.
—Larry David, “The Deal,” Seinfeld, May 02, 1991
Notes
If the slightly pejorative term relationshippy has traction in the culture (and I think it does), it might be thanks to its cameo appearance in the Seinfeld episode The Deal, which aired on May 2, 1991 (see the earliest citation). For the record, here's the rest of the conversation (where George is helping Jerry buy Elaine a birthday present after the latter two slept together):

George: Okay, what about a nice frame? With a picture of another guy in it. Frame says I care for you, but if you wanna get serious, perhaps you'd be interested in someone like this.

Jerry: Nice looking fellow.

George: What about candle holders?

Jerry: Too romantic.

George: Lingerie?

Jerry: Too sexual.

George: Waffle maker.

Jerry: Too domestic.

George: Bust of Nelson Rockefeller.

Jerry: Too Gubernatorial.