To clarify my votes:
I think that too much background is a problem when it interferes with the GM's ability to use hooks to draw the character into the larger milieu. A warning sign comes if the campaign framework must be restructured in more than minor ways to accommodate the individual. Some tailoring is fine and natural, but rebuilding is not.
I think that there is an optimal degree of characterization, centered on personality and typical behavior of the PC in situations that are likely to come up in actual roleplaying. It is NOT centered on bloviation about microdetails of the very special history of a lineage, country, culture, or religion. Probably this optimal characterization occupies just 1/4 or 1/2 of a page--at the beginning of play. As a PC develops over time (and I take that to be an inherent good in roleplaying), that backstory will expand organically, but initially I think less is more.
That said, I think that too little characterization up front is a slight problem in an of itself, but more importantly indicates that the player may not be giving due attention to a key aspect of roleplaying (in my opinion). If a player seems not to "get it", that is probably a harbinger of larger problems to come. When players and GM do not all sufficiently agree about what is important in their game, dissatisfaction (trouble) is bound to follow, unfortunately.