what happens if baby neck is not supported and “falls back”?

Perhaps use your arm to support the head and neck instead of your hand/wrist? A lot less tiring for you. If he’s struggling, either cradle him in your arms and hold him close to you, or carry upright with his chin resting on your shoulder and his body pressed against yours (your other hand will gently support his head so it doesn’t flop, but you don’t actually put weight on that hand). Another awesome alternative for struggling babies is simply to swaddle then well. A night tight swaddle keeps all the limbs inside. Heh. If you find it hard to wrap the swaddle well, consider getting the velcro/zip ones. Very useful for handling struggling babies, as well as for putting them to sleep/nap:)