Don't get me wrong. His overall arc from a mumbling, dog-like sidekick to a cheeky, erudite badass is fascinating. What bothers me about his character arc in the third film though is how much more of one he gets than his partner-in-crime Pintel. Practically every scene in At World's End that features these two has Ragetti upstaging Pintel, getting the spotlight without him, and generally being treated like he's a way more important character.
Pintel and Ragetti aren't the only character duo in film to have balancing issues. Fans of the Hobbit films often point out how much more focus the dwarf Kili gets over his brother Fili despite them being a pair. The roles of Merry and Pippin in The Lord of the Rings are pretty equal in the books and don't change much in the films, but it's clear from the staging and editing that the filmmakers liked Pippin more. I even think that Jake in the first Blues Brothers movie gets the spotlight a few too many more times than Elwood. Why does this happen?
In some cases, it may be in response to fan preference. Jake Blues was played by John Belushi in the original Blues Brothers sketches on Saturday Night Live, and Belushi was a more energetic performer than his costar Dan Aykroyd. Because of this, Jake was probably more memorable and more liked by viewers than Elwood, so the writers decided to give Jake more material when it came time to write the film. Similarly, Ragetti's wooden eyeball and more sympathetic portrayal in the first Pirates of the Caribbean probably made him stand out more than Pintel, so the writers expanded his role in the sequels to appease fans.
Another reason why duos lose their balance could be that one member just shows more potential for personal growth. Kili, Pippin, and even Ragetti are the younger and more naive halves of their duos, so they naturally have more to learn and more growing up to do. That often speaks more to writers, which is fine, but as the writer, you have to do something with the other duo member to offset the more compelling one's growth. Duo characters are usually together because they have a unique and firm understanding of one another, so any notable change that one of them undergoes is going to affect the other.
R2-D2 is pretty much the only character that C-3PO can rant and complain around without getting dismissed, and C-3PO is the only major character who can always translate what R2-D2 is saying. Each one can only achieve his full character potential when the other is present because they're the only characters who fully allow one another to have a voice. They're equal opposites who complete each other -- a whirring, beeping, blue and gold yin yang.
The simplest advice I can think of for writing a good, balanced duo is to almost think of it like adopting twins. If you're going to bring a pair into the picture instead of just one character, then you need to be willing to raise both of them. Explore and celebrate the bond that they have, encourage them to be individuals but not to forget each other, and above all else, treat them fairly.