February 24, 1981

THE more scientists study the problem of overweight and the difficulty of shedding extra pounds, the more it seems that brain and body chemistry control the outcome. Stores of fat in the body increase when food intake is persistently greater than the body's energy use, but controls over this are complex. They involve a constellation of hormonal and nervous system factors, orchestrated ultimately by the hypothalamus, a deep-seated portion of the brain that is involved with emotion as well as basic physiological controls. By studying such controls and the ways in which they can go awry, scientists look toward a future that might provide new approaches to mastering obesity. The attention of many scientists today is focused on the biochemical controls over the fat cells and related aspects of fat storage.

In the wilderness of the Empty Quarter, amid red sand dunes that rise hundreds of feet and where the mercury can soar above 140 degrees, the working day never ends for Don Harday and Roy Korbut, both Canadian nationals. On an around-theclock basis, they drill for oil, certain that it lies miles below these sandy wastes but unsure exactly where. Drilling for oil here is difficult business, and so, too, is getting drillers to come to Saudi Arabia, according to the Arabian American Oil Company, which produces nearly all the crude oil in this country of eight million people. Because of the problems in finding workers Aramco has embarked on a new recruiting drive in the United States and Europe and is stepping up its program to recruit and train Saudi nationals.

The house that Darryl F. Zanuck built contains far more riches than meet the casual eye. The rabid interest among a band of corporate suitors of the 20th Century-Fox Film Corporation stretches beyond a simple desire to be part of the glitter and glamour of making movies. Tucked within the framework of the big film company is a bevy of lucrative assets, including some of the choicest real estate in the world, most of which is carried on the Fox books at well below what the assets might fetch in today's marketplace. It comes as little surprise, then, that Marvin Davis, a Denver oil millionaire, has offered close to $700 million to buy Fox. ''If you took all the assets of this company and sold them off piecemeal,'' says Anthony Hoffman, a securities analyst at A.G. Becker, ''you'd probably get a good deal more money than Mr. Davis is preparing to pay.''

Faced with increasing competition from cheaper sources of credit, most of the nation's large banks yesterday reduced their prime lending rates by half a percentage point, to 19 percent, and several dropped to the 18 1/2 percent level. Bankers cautioned that yesterday's decline in this key rate did not necessarily indicate that lending rates would drop further. They said they remained wary about the immediate economic outlook, and they also expressed concern about President Reagan's economic program. ''We have a nagging fear that the recent leveling off of the money supply will turn around again because the economy has been behaving so much more strongly than we had expected,'' said Frederick W. Deming, senior vice president of the Chemical Bank.

Despite unhappiness about proposed cuts in Federal funds for Medicaid, the Governors of 48 states met today with President Reagan to assure him that they generally supported his efforts to ''restore balance to the Federal system,'' as Gov. George Busbee of Georgia put it. Mr. Busbee, chairman of the National Governors Association, said the Governors were as determined as the President to see that the role of the states was enhanced and the Federal Government's influence reduced. Difference of Opinion But he said they had told Mr. Reagan that they took a view different from his on how to carry out those goals, believing that while the states should be responsible for law enforcement or education, the Federal Government should pay the costs of such transfer payment programs as welfare and Medicaid, the Federal-state program that pays health-care costs for the poor. Mr. Busbee said it was clear that Mr. Reagan did not now believe in a strong Federal role in Medicaid or welfare. ''But,'' he said, ''they're listening and we're making our points.'''