Brine is my favorite character for a number of reasons.
The first one should be fairly obvious: Brine is fun because he's a silly, cute character. I make him do things because I think they're one of those two things. For example, Brine is greedy to the point that it's funny, but not really past that point: ie he loves treasure and always wants all of whatever the party finds, but he does agree to share loot with party members and doesn't try to steal from them. Likewise, Brine is perpetually hungry, and wants to eat all kinds of different things and creatures: it doesn't actually make much sense for a creature the size of a cat to be this way, but it's an easy character trait to play for laughs. Likewise, in the last session Brine decided to spend a couple of free evenings asking the High Priestess of a house of sacred prostitutes a bunch of mundane questions because I liked the thematic juxtaposition of the PC and NPC: the scene, even though we didn't play it out, just seemed bizarrely funny in my head.
Brine doesn't actually need to be anything more than that. Sure, he has a combat function as the party tank, but I do believe the group would be successful without him: albeit it would take longer, and be more risky.
But I didn't leave Brine at that. The first thing I did, with GM permission, was to create a sort of "racial memory" for Brine. The basic reason for doing this was so that I could get away with playing an infant (that said his first words to the PCs) that somehow had the reasoning capabilities of an adult. I don't like playing morons, and Brine's mental stats even after racial penalties compare favorably to the average human's. Just as important as actual mental capacity, having a sort of racial memory gave Brine a pool of experience to draw upon, which has actually been a lot of fun to play around with. Most notably, Brine has some success predicting how one of the other party members behaves, because she behaves in a way that I believe would be similar to adult female black dragons. On the other hand, it also means that I get to have some fun with the things Brine does not know: he might have a working understanding of how to read and write a number of languages, but he had to learn how to actually negotiate and haggle: his evil dragon ancestors never really engaged in this behavior with humans, so Brine didn't know how it worked. So part of the fun I have is figuring out where those boundaries exist, and how to play with them.
The racial memory actually led to some interesting ideas. I consider it the case that Brine tolerates being alone better than most other creatures not just because he is somewhat predatory, but also because his racial memory means that he always has at least impressions of others in his head, even though they aren't as real as the genuine article.
I've also given Brine bigger, more idealistic goals. He dreams of reuniting his parents and family, and even more he dreams of a broader unity amongst dragons. Several of the other PCs have similar stories of family dissolution, so it sort of fit into the party theme. In addition, Brine needed to be removed from a family structure so that he could be viable: the group couldn't have adopted him if they had to worry about a parent breathing down their necks (especially with acidic breath).
For ease of play and theme the game doesn't focus on the difficulties Brine would actually be likely to experience walking around the average city. It helps that we are in a fairly lawless part of the world, but even so a cat sized creature with knife-hard claws and a certain predisposition for violence would be treated with a large degree of trepidation, if not outright hostility. But that interaction with "civilized society" is an important part of what Brine is all about: Brine believes that he has to interact with civilized people to prosper and grow in the world, even though he has a hard time seeing himself as one of them, and they probably feel a bit the same.
One concrete example of this is that Brine has gone out of his way to avoid being defined as a member/officer of the pirate crew, even though he lives on the ship, participates in their fights, and receives a share of the loot. Part of that is that is his basic chaotic nature, but also feeling weird being involved in a crew.
...I've run out of steam for writing, so I think that I'll leave things incomplete. Brine is like that, too: a project I'm frequently turning over in my head and trying to improve.