President Reagan's reappraisal of Middle East policy, forced on him by the departure of Alexander M. Haig Jr. as secretary of state, gives Defense Secretary Caspar W. Weinberger a fresh chance to argue for more "balance" in dealing with Israel and the Arab countries.

The essence of the Weinberger case is that the United States needs all the friends it can get in the Middle East and must woo them whether Israel likes it or not. He believes the United States cannot tolerate destabilizing actions in the region like Israel's thrust into Lebanon and shelling of Beirut.

While conceding that it is too early to know how Reagan may change Middle East policy, officials familiar with Weinberger's thinking predict he will make these recommendations:

* Rein in Israel. One official in the Weinberger camp said Israel's invasion of Lebanon and pounding of Beirut has brought a torrent of protest from Arab leaders to U.S. embassies abroad and to the State Department. King Fahd of Saudi Arabia "called our embassy and asked, 'Do you want to destroy us all?' The Egyptians, Jordanians, Kuwaitis, Bahrainis -- everybody is saying the Israeli attacks on the Palestinians 'will sweep us all away.'"

The official said Arab leaders fear that they will be deposed by their people, if not their political opponents, if Israel is not checked. They also warn that they cannot afford to be seen as friendly to the United States as long as Washington continues to allow Israel to shell Lebanese cities.

Weinberger, interviewed by The Washington Post last week, steered clear of saying anything about punishing Israel for its attacks on Lebanon with American weapons. He would not go beyond stating that an investigation is under way on whether Israel violated the conditions of U.S. weapons sales by using them in an offensive rather than defensive operation. But in the privacy of White House policy sessions he is expected to take a hard line on recent Israeli behavior.

* Widen the dialogue and relationships with the Arab world. In trips to Saudi Arabia, Oman and Jordan this year, Weinberger made progress in this direction. One official said that a better dialogue with Iraq is being sought as well. Bahrain, which Weinberger considers a key Persian Gulf nation, would get as much help as the administration could extend without making it unacceptably visible. An attempted coup against the pro-western government in Bahrain threw a scare into the Pentagon and impelled defense officials to worry more about internal subversion in Persian Gulf countries than intervention from outside by the Soviets or their surrogates.The Pentagon is trying to redirect its military assistance to cope first with internal threats and second with outside attacks.

* Accelerate weapon sales to friendly Arab nations. Weinberger and his allies are convinced that the Israeli have an overwhelming edge in military power in the Middle East and that it is time to make its neighbors feel more secure, partly through selling them weapons. But selling Arab nations weapons at a faster pace would require overcoming substantial political opposition in Congress.

The Weinberger approach to the Middle East has been spelled out in public and in secret guidance he recently issued to the military services to help them plan their budgets for the next five years.

"I would describe it," he said of his approach to the Middle East, "as pursuing the policy in which the friendship and the needs and the problems of several friends of the United States are being considered, with the clear objective in mind that we need several friends and that we aren't going to be able to obtain them if we are viewed as solely being interested in having one."

In discussing the Middle East and Southwest Asia in strictly military rather than political terms, Weinberger's guidance to the armed services states that "our principal objectives are to assure the continued access to Persian Gulf oil and to prevent the Soviets from acquiring political military control of the oil directly or through proxies. To achieve these goals, we must allocate a disproportionately larger investment in this region, and we must upgrade our capabilities to project forces to, and operate them in, the region. We should also urgently increase and improve the capabilities of friendly indigenous forces."