There have been months and months of data entered into these threads with link after link of logical and empirical data on all of this and you now ask for sources...take the time to go back and read the thousands upon thousands of posts across multiple threads - there you will find your sources...these freedom fighters are way beyond catching you up.
Examples include:
1) The claim that Obama spent millions of dollars on getting birther lawsuits dismissed.
2) The claim that the certification of live birth that Obama made available to some media outlets is not accepted by the state department as proof of US birth.
3) The claim that Hawaii doesn't accept the certification of live birth as proof of Hawaiian birth.
4) The claim that babies born overseas could get a Hawaiian birth certificate in 1961.
There is not a single shred of evidence to back up claim 1. Claims 2-4 can be prove false with a relatively simple search over the internet. Yet many freepers accept all of the above claims as if they were gospel truth.