It isn't as though the Chief Justice gets an extra vote or anything...what IS the big deal about being Chief Justice anyway?
The big deal is that the chief justice assigns the cases to various associate justices, thus trying to shape decisions by putting the right players in the right place.
If Burger did NOT vote in the majority, then the senior justice in the majority (William O. Douglas at that time) would have assigned the decision writing. In that event, the decision might have been competently and coherently written by Douglas's wife or by any pro-abort more capable than Blackmun. In his last published opinion on abortion, Burger admitted that he had long believed Roe vs. Wade to have been wrongly decided and dissented for the first time against abortion to prove it.
CJ = 1.5 AJ. Just my guess.