I agree with you, but you are using the wrong numbers.

Sure, only 23% of households have 4+ members, but they contain 44% of all Americans. Likewise, the 1.3% of households with 7+ members contain 6.2% of Americans.

And there are more people in households of 6+ members than in single-member households.

  #people_in_household  %_of_households  %_of_people
  1                     28%              11%
  2                     34%              27%
  3                     15%              18%
  4                     13%              20%
  5                      6%              12%
  6                      2.2%             5.3%
  7+                     1.3%             6.2%

Collapsed to your categories:

  #people_in_household  %_of_households  %_of_people
  1-3                   77%              56%
  4-6                   21%              38%
  7+                     1.3%             6.2%

(source: https://www.census.gov/data/tables/2016/demo/families/cps-20... where tables C1 and A1 give a total 2016 population of 318579k. Table H1 gives numbers of households with 1-6 members, which, by multiplication, hold 298913k people. The remaining 19666k people must be in 7+ member households. This matches table AVG1's 2.53 people/household and surprisingly implies that the 1.6M households with 7+ people contain 12 people on average.)