This makes me wonder exactly which charts from each year haven't been played yet and which year has the most different charts played as well as which one has the least.
Ask and ye shall receive...
These are what remain to be uncovered (at least, since February 2012 - any Billboard charts that may have aired prior to then aren't accounted for here). These standings reflect that 5/26/84 is the chart to be aired next week (barring another sudden change):
1980 - 1/12, 1/19, 2/2, 3/1, 3/15, 3/22, 3/29, 5/17, 5/24, 5/31, 6/7, 6/14, 7/19, 8/2, 8/9, 8/16, 8/23, 10/11, 10/18, 10/25, 12/20, 12/27 (22 of 52)
1981 - 1/3*, 1/17, 1/31, 3/28, 4/18, 5/2, 6/27, 7/25, 8/15, 8/29, 9/5, 9/12, 10/3, 10/10, 11/14, 12/26 (16 of 52)
1982 - 1/2*, 1/30, 2/20, 2/27, 3/27, 4/10, 5/1, 5/8, 5/22, 6/5, 6/12, 7/10, 7/17, 8/14, 8/28, 9/18, 9/25, 10/16, 10/30, 12/4, 12/18 (21 of 52)
1983 - 1/1*, 1/8, 1/29, 2/26, 4/16, 4/23, 5/14, 5/28, 6/25, 7/2, 7/23, 8/20, 9/3, 9/17, 10/8, 10/15, 11/12, 11/19, 12/3, 12/10, 12/31* (21 of 53)
1984 - 1/7, 1/14, 1/28, 2/4, 2/18, 3/24, 4/7, 4/14, 4/28, 5/12, 6/23, 6/30, 7/21, 8/4, 9/15, 9/22, 9/29, 10/20, 10/27, 11/3, 11/24, 12/1, 12/29* (23 of 52)
1985 - 1/5, 1/12, 1/19, 3/9, 3/16, 3/30, 5/4, 5/25, 6/1, 6/8, 7/13, 7/27, 8/3, 8/10, 8/24, 9/7, 9/28, 10/26, 11/2, 11/9, 12/7, 12/14, 12/28 (23 of 52)
1986 - 2/1, 2/15, 4/12, 4/19, 5/3, 5/24, 6/21, 6/28, 7/12, 8/30, 9/6, 9/13, 10/11, 11/8, 11/15, 11/22, 12/13, 12/27 (18 of 52)
1987 - 1/3*, 1/10, 2/7, 2/14, 3/21, 4/11, 4/25, 5/9, 5/23, 6/13, 7/11, 8/1, 8/8, 8/15, 8/22, 10/3, 10/10, 10/24, 11/28, 12/12, 12/26 (21 of 52)
1988 - 1/2*, 1/16, 1/23, 1/30, 2/6, 2/27, 3/5, 3/26, 4/2, 4/9, 5/28, 6/11, 6/18, 6/25, 7/2, 7/23, 8/20, 8/27, 9/3, 9/10, 10/29, 11/5, 11/12, 11/26 (24 of 53)
1989 - 2/18, 3/18, 4/1, 4/29, 5/6, 5/13, 5/27, 7/8, 7/15, 7/22, 8/26, 9/23, 9/30, 10/14, 11/25, 12/2, 12/9, 12/23, 12/30* (19 of 52)
* = "Frozen" week
DISCLAIMER: I took the liberty of counting "frozen" weeks that repeat the chart of the weeks before them, separately from those original chart weeks. To give an example, this is why 12/31/83 is listed but not 12/24, as 12/24 has aired three times on the weeks beginning on the Fridays of 12/26/2014, 12/25/2015, and 12/22/2017 - it's highly unlikely that any one of those airings would use a regular, unfrozen, 12/31 chart otherwise. Similarly, the latest 1985 has ever aired during a given year was on the week beginning the Friday of 12/23/2016 - which had 12/21/85, thus why 12/28/85 is listed but 1/4/86 (the "frozen" week that is otherwise identical to 12/28 which aired on the weeks beginning the Fridays of 1/4/2013 and 1/3/2014) is not. I realize that, quite possibly, no one else would account for those such airings like this - nonetheless, I choose to do so.
Observations:
I'll bet no one expected 1981 to have the fewest weeks left to air, did they? That seems to be the year that is least likely to have a chart week repeated that's already been done - it's tied with 1987 as having the fewest chart weeks that are members of the (exactly) Two Times Played Club, with 5 apiece. But 1987 also has four chart weeks that are Three Times Played and one (1/31) that is Four, while 1981 has just two Three Times Played weeks and nothing further.
1981 is also one of four years to have as few as two chart weeks that are at least Three Times Played, the others being 1980, 1985, and 1986. Until last month, all three of those were like 1981 in having nothing further than that - that is, until 4/13/85 crossed over into the Four Times Played Club. However, all three of those do have more Two Times Played weeks than 1981 does - 1980 has 11, 1985 has 10, 1986 has 8.