UPDATED 2023: Full data for the weeks ending December 27, 1981 and September 5, 1982 has now been added using data transposed from the Nielsen Pocketpiece.
Below are the full weekly ratings results for the entire 1981-82 television season. Viewership wasn't reported by Nielsen until the fall 1988 season, so up until that point the only metric widely available was the household rating (which is what is reported here in this article). To calculate the estimated number of households watching, just multiply each rating by 799,000 (through w/e October 4) or 815,000 (w/e October 11 onward) as that is what 1 rating point represents. The following are newspaper clippings from the Los Angeles Times, which was the only newspaper in the United States to publish full weekly TV ratings results.
Source: Nielsen Media Research via The Los Angeles Times, Fort Worth Star-Telegram & Pittsburgh Press