A battered Alexander M. Haig Jr. leaves tonight on his first overseas trip as secretary of state, seeking to prove his mettle in the complex and volatile region that is the Middle East.

After two devastating weeks in the Washington arena, Haig can hardly afford additional blows to the leadership position he established in the early weeks of the Reagan administration. But the troubled Middle East, where he takes his commanding presence and his entourage this weekend, is full of potholes and pitfalls for a new American statesman.

Haig's objectives on his journey, as described to reporters yesterday by a senior State Department official, add up to a modest start on renewing or repairing important U.S. relationships with Egypt, Isreal, Jordan and Saudi Arabia.

Haig will also visit Spain, Britain, France and West Germany in the whirlwind tour scheduled to encompass eight countries in nine days.

All along the way, Haig's words and deeds will be closely scrutinized for what they tell of his position within the Reagan administration as well as what they suggest about relations between the United States and the world outside.

The first set of questions is the legacy of unexpected and, for Haig, unfortunate collisions that prompted him to draft a letter of resignation to President Reagan 10 days ago and made him the target of national criticism following the attack on Reagan Monday.

The challenging trip, which could improve or further damage Haig's fortunes, had its origins in a request by Israeli Prime Minister Menachem Begin for dramatic action by the United States this spring to bring to life the Palestinian autonomy talks, the next phases of the Camp David peace process.

Begin was interested in high-profile moves to back up the peace process, possibly including trips to Washington by himself and Egyptian President Anwar Sadat, before the Israeli election June 30 in which Begin's political future is at risk.

In late February, the Reagan administration decided that Haig should visit the Middle East this spring as a substitute for the initiatives that Begin was suggesting.

The trip was intended to display American interest without committing the administration to a peace posture in advance of the Israeli elections, and to initiate the top-level contacts that will be the basis for Middle East diplomacy in the months to come.

Once authorized and announced, the Haig journey began to take on a life of its own within the American government, being used as a deadline for decisions on the ground that the secretary of state needed to bring authoritative positions.

Among the most sensitive questions was the F15 enhancement equipment and other sophisticated military gear requested by Saudi Arabia during the last year of the Carter administration, and considered by the Saudis as a "litmus test" of their American military connection.

The Reagan administration announced a decision in principle early in March to sell most of the gear the Saudis requested and to supply additional military credits to Israel as a form of compensation.

As the Haig trip approached, an internal policy debate culminating in a National Security Council meeting Wednesday afternoon centered on the timing of final proposals to Congress for the controversial sales.

From the point of view of Saudi policy, it would be desirable for Haig to bring concrete administration decisions to Saudi leaders in Riyadh next Tuesday. But two days before that, Haig must pass through Jerusalem, and those same decisions could fuel an unpleasant confrontation with Israeli leaders.

A large group of members of Congress, in the meantime, is ready to begin a loud and lengthy debate the minute that the Saudi proposals go to Capitol Hill, especially the proposal for sale of AWACS, the radar-equipped, command-and-control aircraft.

The U.S. military, according to informed sources, has recommended -- and the Reagan administration is likely to approve -- the sale of five AWACS aircraft and seven KC135 tankers for inflight refueling on the Saudi defense package previously approved in principle.

But official sources said that, despite pressure to the contrary from the Pentagon, final decisions on key issues have been deferred until Haig returns, in order to avoid starbursts of controversies during his journey.

Another sensitive issue is the U.S. role in a multi-national peace-keeping force to police the Sinai after the Israeli withdrawal scheduled for next April. The Camp David peace treaty called for a U.N. force to do the job, but President Carter promised Israel that the United States could organize a multinational force in case the U.N. refused to participate.

Haig is said to favor a permanent U.S. military presence in the Middle East as the best means of projecting American power to the area, and some officials close to him are reported, for this reason, to be eager for American troops to be stationed in a Sinai peace-keeping unit.

The more this has been discussed in Washington, however, the more resistance has been created in Cairo and some other Middle East capitals.

The senior State Department official who briefed reporters yesterday said the United States is ready to limit the mission of any U.S. troops in a multilateral force to policing of the Israeli-Egyptian treaty, thus ruling out their use in other troubles of the region.

The official, who cannot be named under the rules of the briefing, said the "informal consensus" is that 2,000 to 4,000 peace-keeping troops will be required in the Sinai, with "no more than 50 percent" to be supplied by the United States.

Haig is expected to try to advance the framework if not the final details of a Sinai peace-keeping force in his talks with Sadat Sunday and Monday. But a decision to station U.S. forces in the troubled area on a long-term basis, possibly under instructions to shoot back if trouble starts, is likely to generate controversy in Congress.

Haig, who speaks in global strategic terms, is said to be seeking a consensus in the area about the Soviet threat. The countries he will visit all agree on that, in general terms.

But they do not agree on how to work with one another, or how to proceed with the United States on the knotty issues of peace, Palestinians and regional tensions in the Middle East.