Short answer: no part.
What was the justification? The courts believed they saw a right to privacy in the Fourth Amendment that suggested that a woman can kill her unborn child in utero. Here is the Fourth Amendment:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
Do you see any indication here that the framers of the Constitution believed that women had the right to abort their children? Me neither.
Perhaps it could be argued that, if a woman did such a thing in private in her own home there might be Fourth Amendment protection – though if that was the case, a husband could also kill his wife in the privacy of their own home.
However, women don’t even abort their children in their homes. This is a thing done in public, in exchange for Federal Reserve notes, which places the activities under the jurisdiction of the government that circulates Federal Reserve notes.
Even if you believe abortion should be legal, please think logically about this: there is no Constitutional justification for legalized abortion.
We have come to accept much deception and obfuscation from the US government in the performance of their duties. In many instances office holders have failed to honor their vows to defend the US Constitution, instead constantly searching for ways to undermine it. This is the time to acknowledge how we have been tricked and disenfranchised. This is the time of the Great Awakening.