The nation's largest industries showed strong quarterly earnings in reports issued yesterday.

Three major chemical companies reported improved first three months of 1978, when the industry was plagued by severe weather, a prolonged coal strike and losses in foreign-exchange transactions.

Union Carbide, the nation's largest petrochemical and plastics company and the second-largest chemical producer, reported a 58 percent increase in quarterly earnings, $124.9 million ($1.91) over the year-ago period of $78.9 million ($1.22).

Union Carbide had to pay more for fuel and raw materials, but that expense was offset by higher profits in other operations, such as producing metals, said chairman William Sneath.

W. R. Grace & Co., a New York-bases company with chemical, consumer-products and natural-resource operations, said earnings jumped 56.2 percent to $55.1 million ($1.30). That compares with $3.3 million (86 cents) in the first quarter of last year. Sales for the period were $1.14 billion, up 14.5 percent from $99.7 million.

Olin Corp., based in Stamford, Conn., said first-quarter earnings were $7.5 million (73 cents) over the year-ago period of $3.8 million (16 cents). Sales rose to $437 million in the 1978 quarter.

Olin owns Winchester Ltd., producers of sporting arms, ammunition, skis and other outdoor recreation products. It also owns Ecusta Paper & Film, which makes cellulose paper and cellophane.

Weyerhaeuser Co., the lumber giant, said, it earned 94 cents a share in the first quarter, up from 51 cents a year ago, as sales rose to $1,008 billion from $804,12 million.

Net income rose to $193.29 million from $136.18 million.

Weyerhaeuser also announced it is making an offer of $610 million for Bodcaw Co., the Dallas natural resources firm, for which Mobil Corp., has offered $550 million cash. The offer is $135 million higher than Mobil's alternative preferred share offer, Weyerhawuser said.

Bodcaw owns 300,000 acres of timberlands in north central Louisiana, which are Weyerhaueser's immediate objective.

The 3M Co. had a 27.5 percent gain in profit in the first quarter on a 20.4 percent rise in sales.

Net income was $152.1 million ($1.30) on sales of $1.305 billion compared with $119.3 million ($1.03) a year ago on sales of $1.084 billion.

Chairman Raymond H. Herzog said 3 M's price increases for the year averaged 3 percent, well within President Carter's voluntary guidelines and under the current inflation rate.

The big profit gains, he said, came from 3 M's international operations. In the United States, unit volume was enhanced by some advance buying by customers fearful of work stoppages that could cause shortages.

Dillingham Corp., the conglomerate, earned $10.11 million (77 cents) in the first quarter in contrast with a loss of $603,000 a year ago.

Revenues rose to $251.61 million from $213.45 million.

The 1978 first quarter loss was caused by writedowns on a large LP gas inventory and foreign currency long-term debt of the company's 50 percent owned Pacific Norse Shippling Ltd., a dry bulk carrier line.

Wheeling-Pittsburgh Steel Corp., reported net income of $9.16 million ($2.20) for the first quarter of 1979.

That compared with a loss of $18.1 million ($5.04) for the same period of 1978.

Wheeling-Pittsburgh's first-quarter sales of $313.4 million were 20 percent over sales of $262.1 million in the same period last year. First quarter shipments of 763,569 tons were 10 percent above the 695,103 tons shipped in the first three months last year.

First quarter earnings for Burlinton Northern Inc. rose 28percent, from $31.9 million ($2.39) in 1978 to $40.7 million ($3.13) in 1979.

Earnings for the three months ended March 31 include a $6.8 million reduction in deferred income taxes.

Strong performances by the resources division and by Burlington Northern Air Freight helped offset the effects of severe winter weather on the railroad, which had operating expenses 14 percent above last year's for January and February.

The railroad rebounded in March, however, posting 6.4 percent revenue ton-mile increase over the strong March 1978 traffic.