He has released a valid birth certificate, specifically in response to the question of his eligibility.
He hasn't spent money to block release of documents. He's spent money (in the sense that some lawyers have gotten paid, it's doubtful that Obama spent his own money) responding to lawsuits that were filed. He has to respond to a lawsuit, there's really no choice there. The expenses there have been pretty minimal. Aruging motions to dismiss, which have all been successful.
The so-called birth certificate shown on his website during
the campaign was NOT valid. All he has to do to end this
doubt is show a valid birth certificate, signed by a doctor!
Incidently, since his father was a british subject, at the time of his birth and his mother was too young to confer
citizenship; Obama is a british subject.