A sweater wrapped around her shoulders and an electric space heater glowing at her feet, 71-year-old Hattie Patterson sat in her wheelchair, describing the strain of $100-a-month utility bills on a $311 monthly Social Security check, and watching as workers at her Takoma Park home installed storm windows, weatherstripping and other energy-saving devices aimed at cutting those bills by at least one-quarter.

Patterson's home of 20 years is being "weatherized" under a state program designed to trim the heating bills of low-income residents to more manageable proportions. State officials estimate that some 115,000 low-income families live in homes that need weatherizing, out of a total of 215,000 families eligible for such aid. Each home currently wastes about $200 worth of energy annually, they said, a total energy drain of more than $23 million.

At the current rate of caulking, sealing and insulating, according to a Baltimore-based weatherization group, it would take more than 21 years to complete the work statewide. The backlog locally is even greater, at 66 years in Prince George's County and 55 years in Montgomery County, the group estimates.

Often living in older, draftier homes, "poor families in Maryland are spending 16 percent of their income on energy, compared to four percent for other families," Ruth Massinga, secretary of the state Department of Human Resources, told a gathering of about 20 legislators, state and county officials, and community activists yesterday. "If in fact families must spend that percentage of their incomes," she added, "they are in considerable trouble."

Patterson, for example, has gone without central heat and hot water since her gas was turned off more than a year ago and she lost her electricity last summer until she received an emergency grant from the state to have it turned back on. She manages to keep warm, Patterson said, with three space heaters and a rug bundled against the front door to keep out the cold air that sails through a gap at the bottom.

Patterson's home was one of three stops on a tour sponsored by community groups supporting a bill, to be introduced in the Maryland General Assembly next month, that would require utility companies to contribute .3 percent of their gross revenues to help poor families weatherize their homes.

The $10 million in federal funds that Maryland has to spend this year on weatherizing the homes of low-income people "doesn't go very far," said Cheryl Grice, who directs the state's weatherization program. Fewer than 9,000 homes are expected to be weatherized. Next year's funding is below $7 million, and the Reagan administration, in its latest round of budget cuts, is proposing to phase out the program entirely by 1990.

Utility companies are far from thrilled with the .3 percent proposal. "We think the appropriate way to go about about raising money for a weatherization program -- if a program is needed -- is to raise it through tax dollars" rather than through "forced contributions" from utility customers, said Thomas A. Julia of Washington Gas Light Co., which estimates the bill would cost customers as much as $1.5 million annually.

At the Silver Spring apartment of Glenna Liston, windows decorated with red and green Christmas designs were covered with sheets of 8-millimeter thick plastic, part of a program operated by Neighbors Together, a Silver Spring tenants organization. Funded with $14,500 from Montgomery County and $25,500 from Pepco, the program will provide weatherization for 130 low-income residents of Takoma Park and East Silver Spring.

Last year, "that front window there in the winter was covered with ice that thick, and it made the house so cold I had to turn the heat clear up to 70 before I was comfortable," said Liston, 66. Since the plastic sheeting was installed last week, she said, "my apartment has been really warm. I turned the heat down to 60 since they put it on."