05AB1E, 67 bytes

ʒKæOyå

ʒKæ¦Oyå

Try it online! or Try all cases!Try it online!

ʒ       # keep numbers of the input where:
 K      # the input with the number removed
  æ     # all subsets of this
   O¦    # remove the first subset (the empty list)
    O   # the sums of the subsets
    yå yå # contain the current number

05AB1E, 86 bytes

æʒg2@}OÃʒKæOyå

Try it online!Try it online! or Try all cases!

æ ʒ       # push thekeep powersetnumbers of the input where:
 ʒK   }   # keep the subsetsinput where:
with the g2@number removed
  æ #   the length# isall <=subsets 2
of this
   O  O  # sumthe eachsums subset
of the subsets
    yå Ã # set intersection withcontain the inputcurrent listnumber