Below are the weekly Nielsen ratings results for the 1979-80 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 763,000 as that is what 1 rating point represents.
Full weekly household ratings for every show weren't made available until 1981, so only partial results are available for this season. Most weeks have the top 20 weekly ratings available, but 2 weeks have only the top 15 (Dec. 23, 1979 & Jan. 13, 1980) and 1 week has only the top 10 (May 4, 1980). The data for the top 20 programs comes from Newsday, data for the top 15 programs comes from The New York Times, and the data for the top 10 comes from the Raleigh News and Observer.
Additionally, the second document includes full rankings (without ratings) from The Fort Worth Star-Telegram and these are available for nearly every week of the proper season (not the summer) except for the following weeks: w/e Dec. 23, 1979 (only top 20), Dec. 30, 1979, Jan. 6, 1980, and May 11, 1980. The final week of full rankings is the week ending May 18, 1980.
ARCHIVED WEEKS (ratings - all weeks)
ARCHIVED WEEKS (full rankings - thru May 18, 1980)
Source: Nielsen Media Research via Newsday, The New York Times, The Raleigh News & Observer, and The Fort Worth Star-Telegram