Why did anyone respect Marbury v. Madison?

Because it was a wise, wellcrafted decision that won respect for the Supreme Court.

The issue was that Marbury had received a federal judge appointment from the outgoing Adams' administration. He was an opponent of the new, Jefferson administration, who was represented by James Madison as Secretary of State, (hence the case of Marbury v. Madison), who had used bureaucratic tactics to hold up Marbury's appointment.

Chief Justice John Marshall's opinion was that Marbury was legally entitled to his appointment (pleasing Adams' Federalists), but that the Supreme Court did not have the Constitutional power to enforce this, that it would have to go back to a lower court (effectively "stopping" the appointment, pleasing the Jeffersonians). The decision also overturned a Congressional law that gave the Supreme Court "original jurisdiction" on the grounds that it was unconstitutional.

Essentially, the Chief Justice of the Supreme Court had voluntarily limited that court's powers. Instead, he claimed for the Supreme Court the privilege of judicial review, but only within the framework established by the Constitution. Because of this posture of adhering to the Constitution, the Supreme Court became highly trusted, having done this better than Congress and the Executive branch. Not even Jefferson could disrespect the Constitution.

Question:
Why did anyone respect Marbury v. Madison?

1. The court is so weak that Jefferson would ignore any ruling against him.
2. The court, essentially, rules against Jefferson indirectly by giving itself the power of judicial review.
3. ???
4. The court has the undisputed power of judicial review.

Short Answer

The Court didn't rule against Jefferson. While it found that Marbury had the right to the office, it found the Congressional law which empowered the supreme court to directly rule on the case unconstitutional, thereby defining the right of the supreme court to deny congressional acts / laws on Constitutional grounds.. Marbury never got to serve in his judicial office and Jefferson's appointments stood. President Jefferson wasn't going to object to the Supreme court saying it didn't have authority to check his actions. And once Jefferson didn't object, the precedent was set. It did't matter that the court was weak in 1801, the next time the supreme court felt the need to rule over congress they had a precedent to cite, one in which the Presidency had already gone along with.

Judicial Review in the United States
After the Court exercised its power of judicial review in Marbury, it avoided striking down a federal statute during the next fifty years. The court would not do so again until Dred Scott v. Sandford, 60 U.S. (19 How.) 393 (1857)

Detailed Answer

Background

Before President John Adams was to leave office, he appointed several people into government positions. William Marbury was one of them. The appointments were not delivered before the next President was sworn into office. So it was the next President, Thomas Jefferson's, responsibility to deliver the appointments. President Jefferson declined to deliver the appointments preferring to appoint his own people rather than the previous President John Adam's choices for these offices.

William Marbury and the others who were refused their appointments sued in the Supreme Court to get their appointments delivered. Marbury's argument depended on a law passed by Congress which gave the Supreme Court the authority to issue a "writ of mandate" against the Presidency, compelling Jefferson to deliver the appointments.

The Ruling

The Court ruled 4-0 that Marbury had the right to his appointment and that the appointment itself was unimportant, Marbury was able to assume his commission without the formal delivery of the paper, given it was signed and all formal procedures other than delivery were followed.

The Court further found that the Congressional Law was unconstitutional and congress didn't have the authority to pass a law giving the supreme court "direct" authority to issue writ's against the Presidency. That in the Constitution, the defined jurisdiction of the supreme court was limited to cases affecting offices in which states were involved.

U.S. Constitution, Article III, Section 2
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.

Thus any case in which the Supreme Court would issue a writs of mandate would have to start in a lower court first.

With that ruling, as you say, the court declared itself powerless in commanding the appointments from the executive, but gave itself the power to declare congressional laws unconstitutional.

the ??? would be that, Jefferson wasn't going to object to the supreme court giving him what he wanted even if tangentially, because of his own self interest. Congress was the big loser in this decision because the Supreme Court in basically granting what the President wanted, set itself above congressional decisions from then on with the Presidency as it's ally. Jefferson got what he wanted. Marbury never held a judicial office and the the precedent was set for the Supreme Court to have the power of constitutional judicial review.

Assuming that you are focusing on how the Supreme Court's wishes were enforced, and how they were unilaterally able to amass so much power for themselves and the rest of the Judicial branch, and having its will enacted by the actual government agents, this is a very good question.

The three branches of the Government have never been absolutely co-equal, and their relative powers have varied over time. Congress's power in the early republic was certainly far greater than taht of the other two, and was relatively more powerful than its current manifestation. Originally, even the president's veto was seen as only being used when the president believed a bill unconstitutional.

There were times, even after Marbury vs Madison, when the court's rulings were flagrantly disregarded. The most notable of these was Worcester V Georgia. President Jackson famously disregarded the court's ruling against a Georgia law that allowed settlers to move into Cherokee land. He said of it "John Marshall has made his decision, let him enforce it", and the Indian Removal Act was carried out regardless. There was in fact only one instance prior to the Civil War in which Judicial Review was explicitly used, when the Missouri Compromise was ruled as unconstitutional in the Dredd Scott case.

So Marshall did not make a habit of invoking Judicial Review, and as JMS noted above, the ruling was in the immediate interests of those in power at the time. For this reason, Judicial Review was not challenged by the other branches at the time, and when it came into common use, federal power had been greatly expanded and changed after the Civil War. After the Civil War, federal authority and nullification of anything that was the Federal Government's custom was an issue that had been completely resolved at bayonet point.

TL;DR: The implications of Marbury v Madison and Judicial Review, which Jefferson failed to forsee, did not become a regular part of American government until a long time later