The CJ decides who writes the opinion of the majority if in the majority, and the dissent if in the dissent. Its the job of the CJ to bring sides together in clear oppositions, and "horse trade" between bits and pieces of a decision so that its clear where a majority/minority lie.

The CJ's foremost political role is to ensure the judicial branch of government is seen as a politically legitimate institution which wields its power against the other branches in a constitutionally and poltiically legitimate way. If that slips, congress can start hiring/firing; and the executive, in the end, controls the guns -- they can be arrested.

To avoid being arrested or fired, the court has to keep all sides believing the rules they set are fair.

They have no power, in the end, but the power they are allowed to have. They govern by consent of the other branches, and that's trivial to take away

So very specifically I've historically read Roberts as a fairly moderate jurist. He has a true romanticism about the neutrality of the court and that it shouldn't be a political body. (This is ridiculous, but anyways.) This has changed as the court has reached a 6/3 bias. When the court was a 5/4, Roberts could swing to the center and bring the majority position with him. But now the far right wing doesn't need his help: The conservative wing can do a 5/4 even with his dissent. So you see Roberts bucking the conservative trend much less, maybe not because he agrees with the court but knows he can't push the outcome to the center.

The other aspect I think in play here is that the current executive branch pretty much just ignores every court order it doesn't like, and the Court can't enforce any ruling it makes, because that's the executive branch's job. I think Roberts knows if the Court pulls against Trump very hard, it could lead to a showdown where Trump just... does what he wants anyways, which would destroy the perceived power of the Court. I think Roberts has tried to dodge a lot of law and a lot of rulings to avoid clear positions on the President which he would, in turn, ignore.