to stretch out: to extend a hand or object outward so that it reaches
Across the Gospels this verb almost always describes one motion: a person stretching out the hand. Jesus stretches out his hand to touch a man with a skin disease (Matthew 8:3), to catch Peter as he starts to sink (Matthew 14:31), and to point toward his disciples as his true family (Matthew 12:49). A man with a shriveled hand is told to stretch it out, and in the stretching it is healed (Matthew 12:13). The word carries no special force of its own; it simply names the outward reach, and the meaning comes from whatever the hand is reaching toward.
The same verb can name a hostile reach. To stretch out a hand "against" someone is to move to seize or arrest them, which is why Jesus tells the crowd that came for him, "you did not stretch out your hands against me" in the temple (Luke 22:53). The nearest Greek word for that grip is ἐπιβάλλω, which likewise pairs with "hand" but for laying hold of a person.
Once the object is not a hand at all. On the storm-tossed ship the sailors pretend to be letting out anchors from the bow (Acts 27:30), where the verb means paying an anchor or line out into the water. And in John 21:18 Jesus tells Peter, "you will stretch out your hands," an ordinary gesture that the Gospel writer presents as a quiet hint of how Peter would die.