"Xenoblade Chronicles implemented a simple relationship system where you could see how accomplishing in world quests affected people's relationships with each other, and how fighting together affected members of the party's relationships with each other. Genius. Simple to implement. Is it really so much to ask? Apparently so."
Fire Emblem has a system sort of like this, but perhaps not as advanced as you want. Characters can develop relationships together (even getting married), and when they do it effects their stats. Characters who have good relationships work better together, and offer better in battle support. It's pretty neat actually. It's one of my favorite game franchises.
Fire Emblem is one of those franchises that I keep meaning to get into... I always feel like I've missed the boat with it. But whenever I see a commercial or review for a game in the franchise I always say, 'Yeah, I want to play that!'
Didn't know that the characters could marry, though. I'll have to revisit that series, for sure.
Fire Emblem Awakening is my favorite one for Nintendo 3DS, but I've also played on Gameboy Advance and Gamecube.