On the infant scale in the pediatric nurse's office, Jessica weighed 14 lbs. 12 oz. At birth seven months ago, her weight was 4 lbs. 11 oz. Jennifer, her twin and next on the scale, was born at 5 lbs. 4 oz. Now she was 15 lbs. 12 oz. "They are way ahead of what they should be," said Angie Olawski, a public- health nurse and recent graduate of Clemson University. "Infants should double their birth weight by six months, so these two are doing well."

The babies' mother was pleased with the news. She has been coming to the Lexington County health center as part of the Women, Infants and Children program. This is the progressive federal program that provided $32 million last year for South Carolina, a state that has the nation's highest rate of infant deaths except for Mississippi and the District of Columbia.

In Lexington County, in industrialized central South Carolina, the parents of low birth-weight babies are overjoyed when their children pull through the first year. The National Academy of Sciences reports that infants weighing "5.5. lbs. or less are almost 40 times more likely to die during their first four weeks of life than the normal birthweight infant."

The costs of saving lives are enormous. A University of West Virginia study found that $100,000 is needed to treat each child admitted to a neonatal intensive-care unit. Forty percent of the children who survive are either physically or mentally impaired, with some form of lifetime care required.

After weighing the twins, Olawski spent about half an hour with them. She administered polio drops orally, gave the first immunizations for diphtheria and tetanus and drew blood to check for iron. The service was comprehensive, qick and efficient. The mother, who came to the clinic with her two other children, was grateful.

The Lexington County center, which is one of South Carolina's largest, had a caseload last year of 1,065 patients served comprehensively. South Carolina's ranking of third in infant mortality is no success story, except that in the past five years the state's death rates have been declining. Public-health officials point to places such as the Lexington center as examples of providing total health care for families. In the past, it was fragmented. One positive result is that South Carolina serves 51 percent of its women and small children eligible for WIC. The state ranks fourth in that category, with northern states -- such seemingly advanced ones as New York, Wisconsin, Illinois and Massachusetts -- among the 42 that serve fewer than half of the eligible.

Nationally, the effects of a cutback in maternal and child health programs are beginning to show up in statistics. Last week the Children's Defense Fund, in a 302-page report called the "Maternal and Child Health Data Book," said that between 1982 and 1983 the infant mortality rate rose by 3 percent. It is the largest one-year increase in 18 years. The data now coming in for 1984 show a 6 percent increase.

Black families are suffering the most. The CDF reports that "the black/white infant mortality gap in 1983 was at its widest in more than 40 years. If the black/white infant mortality rates were equal, about 5,500 black infants would not have died in 1983." In that year, "a black infant in Chicago, Cleveland or Detroit was more likely to die in the first year of life than an infant born in Costa Rica or Cuba."

Officials at the Lexington center in South Carolina are braced for the effects of the retreat in federal services to the poor. One official remarked the other day, half-jokingly, that if you like starting your public-health career at the bottom, South Carolina is the place to be. In fact, a worse location can be found, one that congressional committees need make no field trips to discover: the District of Columbia. In seven of the 10 categories involving child and maternal health, CDF lists the District as among the five worst states. South Carolina is in five of the 10 categories.

The efficient and caring atmosphere in the Lexington County center reflects the attitude of Marie Meglin, the state's director of maternal and child health for the past year. A nurse with a master's degree, she provides an uplifting answer to the question of whatever happened to the '60s civil- rights activists.

Meglin went to Greenwood, Miss., in 1963 and spent five years as a nurse among rural black families. She worked with Martin Luther King and Stokely Carmichael when they came through. From her Mississippi experiences, Meglin decided she could be more effective by becoming a public- health administrator. The early results of her decision are in: a strong WIC program and a decrease in infant mortality. That, plus Jessica and Jennifer, who are going to make it.