National Steel Corp. reported second-quarter earnings of $45.2 million yesterday, up 43 percent over the $31.5 million earned for the same quarter last year.

On a per-share basis, the three-month earnings were $2.34 compared with $1.64 a year earlier. National said the pershare earnings were the third highest of any single quarter in the corporation's 50-year history.

Quarterly sales were $1.1 billion compared with $924.8 million in 1978. Raw steel production, meanwhile, set a corporate record at 3 million tons. Production for the 1978 period amounted to 2.6 million tons.

For the half, National earned $65.9 million ($3.42 a share) on sales of $2.21 billion compared with $34 million (1.77) on sales of $1.77 billion in the first half of 1978.

Production for the half totaled 5.7 million net tons compared with 4.9 million net tons a year earlier.

"We have benefited from a high level of operations at all of our plants resulting from increased demand for our products during the secoind quarter, and we have seen major costcontrol efforts offset some of the cost increases," said National Chairman George Stinson.

Western Airlines Inc. reported a sharp increase in second-quarter earnings yesterday, but Pan American World Airways Inc. said rising fuel costs drove its earnings down.

Western said its net income rose to $14 million ($1.03 a share) from $5.5 million (39 cents) for the year-earlier period.Revenues climbed to $241.3 million from $201.9 million.

But Western's net income for the first half was $26.7 million ($1.96) down from $32.2 million ($2.45) a year earlier.

Western's latest first-half earnings included a $10 million one-time credit, while last year's first half included a $16.2 million credit from an accounting change.

Despite a 9.8 percent rise in revenues, Pan Am said its net income for the quarter ended June 30 dropped to $37.1 million from $46.2 million a year earlier.

Per-share earnings slipped by half, to 52 cents from $1.09 in 1978's second quarter, Pan Am said. Gains from the sale of equipment added $5.6 million to the airline's second-quarter results compared with gains of $8.6 million for the 1978 period.

Still, Pan Am reported a 27.6 percent increase in earnings for the first half to $28.2 million.

Fuel costs for the transcontinental carrier climbed 27 percent over the year-earlier quarter, Pan Am said, adding it burned about the same amount of fuel for both periods.

Pan Am also said second-quarter comparisons were affected by a Northwest Airlines strike in May and June of 1978, which resulted in heavier traffic for Northwest's competitors.

American Express Co. recorded a 12.5 percent rise in second-quarter earnings over the similar 1978 period as sales of travel services were strong despite gasoline problems.

The diversified travel and banking concern reported net income of $91.6 million ($1.29 a share) for the period ending June 30 compared with $81.5 million (1.14) for the second quarter of 1978.

American Express said its 1978 second-quarter earnings had been restated to show accounting changes for property liability companies, increasing the firm's first-half earnings by $2.4 million and revenues by $5.6 million.

For the first six months of this year, the company reported net income of $164.9 million ($2.31) compared with $146.9 million ($2.05) a year earlier.

Second-quarter revenues were $1.15 billion, up 12.7 percent from $1.02 billion in the year-earlier period. Revenues for the first half of 1979 were up 14.6 percent to $2.22 million.

American Brands Inc., a food and tobacco combine, earned $2.41 a share in the second quarter up from $1.58 a year ago, on a rise in sales to $1.353 billion from $1.228 billion.

Net income rose to $72.15 million from $42.54 million.

First-half profit was $141.7 million ($4.86 a share) on sales of $2.775 billion up from $98.34 million ($3.68) on sales of $2.487 billion.

Part of the earnings gain was caused by the acquisition of Franlin Life Insurance Co.

Weyerhaeuser Co. announced record second-quarter earnings yesterday, and the head of the forest products giant said the firm's domestic and overseas markets remain exceptionally strong.

Second-quarter earnings of $1.20 a share were the highest quarterly results Weyerhaeuser has ever had and compare with 90 cents for the same period in 1978 and 94 cents reported for the first quarter of this year.

The high quarterly earnings brought Weyerhaeuser's earning per share for the first half to $2.14, up 52 percent from $1.41 for the comparable period last year.

Net income for the second quarter was $151 million on record sales of $1.1 billion. First-half net income was$271 million on sales of $2.1 billion. Both were company records for the six:month period.

Demand for all the company's export products -- pulp, paperboard, lumber, logs, plywood and wood chips remains strong, said George H. Weyerhaeuser, the firm's president.

Domestic markets for pulp and paper products also are strong, though there has been some softening in demand for bleached paperboards, used in packaging consumer products, he said.

Lumber markets domestically are very strong, but there has been continuing weakness in plywood prices although there has been no reduction in volume demand, he added.

Jos. Schitz Brewing Co. announced a net loss of $1.2 million for the second quarter yesterday and said it was omitting the quarterly dividend of 10 cents a share.

"The directors considered it prudent to conserve the cash utilized for dividends for use in the business," Schitz Chairman and Chief Executive Officer D.F. McKeithan, Jr. said in a statement.

"Sales are off," said Schlitz' vice president for public relations, John A. Rourke, explaining the reason for the decision. Rourke said it was the first time since the 130-year company went public in 1962 that it had omitted paying a dividend.

The brewery reported sales of $305.1 million for the second quarter, 5.9 percent lower than sales of $324 million during the same period last year. Shipments of beer during the second quarter were down 16.5 percent to 5.0 million barrels from 5.9 million barrels last year.

For the six months ended June 30, Schlitz reported a net loss of $2.7 million compared with net earnings of $8.6 million (30 cents) last year.

The company said the 1979 second-quarter figures included an after-tax charge of $4.8 million (16 cents) for the write-off of certain equipment.