Proof number one. His brother, is dead by an illness, or so he says. However, let us remember that one thing Sai has always had is an unexplainable hate for Orochimaru viewing him as nothing but a monster bent on the destruction of Konoha and an evil person. Any anbu especially of Root division can be expected to believe this, but something about Orochimaru has drawn Sai in and he seems to have special hate for this man. If it was Orochimaru who he believes killed, or captured Suigetsu this is a very believable circumstance.
Proof number 2 here is that he says that he was given training identical to that of the forsaken mist tradition. The other person we know to have followed this was Zabuza who was someone suigetsu worked under. Not only that but we also can delve that Root must have watched and probably studied the Mist murder techniques. Follow this by we know Suigetsu is from Mist and it is not unbelievable that they had contact and could have developed a friendship of sorts.
Proof 3 is in the personality type of Suigetsu and Naruto. Suigetsu is very brash and loud like Naruto, he brandishes Zabuza's weapon, threatened Sasuke, started a fight with Kisame, and has no trouble making fun of his other group members which leads to the conclusion he could also be determined unrefined. And Suigetsu is the one seen usually asking "What are we still doing here" After Sasuke fought Deidara and is not one into waiting around and doing nothing, following the example of impatient.
Proof 4 and the last proof is here. The picture of Sai's brother (Notice and it's important to make a note that they are not related by blood as Manga Page 2 proves) looks nearly identical to Suigetsu. The only parts that are different are inhuman, and could very well been acquired while Orochimaru performed tests on him and may be a result of this, or Sai could have always seen him as a human and thus drew him that way. Also notice the sword, which is Suigetsu's weapon of choice.
This leads us to the conclusion that Suigetsu is Sai's brother, with little proof that he could be anyone but. What does this mean for Suigetsu and Sai? Well their relationship is like Naruto and Sasuke's and they aren't real brothers. Also the book sees them fighting for some reason or another. This could lead to Sai betraying Konoha, or more likely a fight to the death between Sai And Suigetsu.
Theory couldn't have been done without help from Amaterasu.