Chief Justice John Roberts also wants to maintain the independence and respect of the judiciary, an increasingly fraught proposition in an era when the Democrats threaten to stack the Court or worse if (realistically, when) they get power. So, throwing the liberals a narrow win in an important case from time to time preemptively stymies and distracts potential forthcoming attacks on the Court and ultimately helps conservatives.
While what you say may be true, I do not agree. That is not Robert’s or the Supreme Court’s purpose - to throw a bone occasionally to Whichever side. It is to decide cased based on the Constitution. If what you say is true, then he is doing exactly what I am saying he is doing. If he really thinks the judiciary is independent as he said when he said there were no Republican and no Democrat judges, then he is either mentally ill, oblivious to reality or just plain dump.