valency

From Late Latin valentia and Latin valentia (“bodily strength; health; vigour”) + English -y (suffix forming abstract nouns denoting a condition, quality, or state). Valentia is derived from valēns (“healthy, strong, vigorous”) + -ia (suffix forming feminine abstract nouns); while valēns is the present active participle of valeō (“to be healthy, sound, or well; to be strong; to have influence or power, etc.”), ultimately from Proto-Indo-European *h₂welh₁- (“to rule; powerful, strong”).

Sense 1 (“combining capacity of an atom”) and sense 3 (“number of arguments a verb can have”) are possibly from valence +‎ -y.