Before rulers and measuring cups, there was the human body. A handful — Old English handful — is one of the oldest measurement compounds in the language, formed from hand + full in the simplest possible way: as much as the hand can hold.
The word hand comes from Proto-Germanic *handuz, whose deeper origins are debated. Some linguists connect it to a Gothic root meaning 'to seize', which would make a hand, etymologically, 'the seizer'. Others see connections to words meaning 'a group of five' — the hand's defining feature.
As a unit of measurement, a handful was genuinely used in medieval trade. It equalled roughly 4 fluid ounces of dry goods, though obviously it varied by hand. The body-based measurement system it belonged to included the foot, the span (outstretched hand width), the cubit (elbow to fingertip), and the fathom (both arms outstretched).
The figurative 'small number' sense appeared by the 15th century — a handful of soldiers, a handful of coins. The 19th century added a further meaning: a person who is a handful is one difficult to manage, as though you were trying to grip something that squirms and resists containment.
The -ful suffix as a quantity marker (cupful, spoonful, plateful, mouthful) is a productive Germanic pattern with no exact parallel in Romance languages.