Obama’s lawyers had Berg’s suit dismissed in the lower courts on the grounds of “lack of standing”. That’s how it got to SCOTUS. This was posted on FR before the election.
Okay, I'll now believe that Obama spent some amount of money on this, since he and the DNC did respond to the lawsuit filed by Berg (and have presumably responded to other lawsuits). That doesn't mean they've spent hundreds of thousands of dollars; I doubt that anyone has any actual knowledge of the amount. My own guess would be in the tens of thousands of dollars -- my brother is an attorney, so I have at least a vague idea of what lawyers might charge to file responses to motions and lawsuits.
But let's assume that they have run up several hundred thousand or even a million in legal fees. Whatever it is, it is hardly indicative of guilt on Obama's part. The suggestion that he could have saved that money by simply producing his original birth certificate is nonsensical. The Berg lawsuit was not just a demand for a birth certificate. It was a demand that Obama be disqualified from being elected President (and also a demand for attorney's fees). Producing a birth certificate wouldn't have made the lawsuit disappear; it would simply have been entered into evidence for a subsequent trial.
Obama's attorneys took the smart (and most cost effective) route by getting the lawsuit dismissed for lack of standing, to avoid the much greater expense of additional depositions and discovery and trial costs.
The whole line of argument -- that only a guilty person would spend a bunch of money defending himself against lawsuits, whereas an innocent person would immediately provide documents in response to lawsuits which that innocent person considered frivolous -- is absurd. Under today's legal system, the respondent in any lawsuit is going to have to spend a lot of money defending himself regardless of its degree of legitimacy.