pair, set, comparison, counter for pairs
双 centers on the idea of two things that belong together: a pair, a set, or a matched comparison. The counter sense is a natural extension for counting paired items.
双 is a simplified form that visually repeats 又 (hand) to represent a pair. Historically, it is related to 雙, which used two birds (隹) to express a pair, but the modern form focuses on the doubled-hand image.
Two identical 又 (hand) shapes side by side: imagine holding up both hands to show a matching pair.
For ソウ, picture a pair of socks: socks -> ソウ, and the two socks are a perfect pair just like the two hands in 双.
twins; twin
both parties; both sides
peerless; unparalleled; unparallelled; matchless
pair
seed leaves (of a dicot); cotyledons; bud; sprout
two-way; bidirectional; interactive
having two poles; bipolar
binoculars; field glasses
both eyes; binocular
double-headed
(two) matchless things; (two) matchless people
twins
race game (board game played with dice in which the object is to reach the end of a track)
distinguished person
identical twins
duality
two-motored
Siamese twins
pair (esp. of folding screens)
unparalleled in Japan, China and India