to let something go from your hands in one quick, decisive motion: to fling, cast, or set it down
The picture behind this verb is a single sharp release. Whatever is in the hand goes, and the person letting it go is not fussing over how it lands. That is why the same word fits a man throwing money away in disgust, a spirit slamming its victim to the floor, and sailors heaving a ship's gear over the side in a storm.
What surprises most readers is that the same verb also covers laying people down. When crowds carry the sick to Jesus and put them at his feet, the word does not mean they were handled roughly. It means they were set down fast, in a rush, with no ceremony and no arranging. The gentleness comes from the scene, not from a different word. The broad verb βάλλω covers both hard throwing and calm placing; this one always keeps the note of speed.
In its completed passive form the verb stops describing an act and starts describing a condition: people who have been thrown down and left where they fell. That is the force of the crowd who look to Jesus like sheep without a shepherd. They are not merely tired; they are dumped and unattended.
Across almost every use there is feeling in the action, and it is the feeling that picks the English word: disgust, panic, fury, or pity.